Lebwohl-Lasher model - Revision history

66.254.229.225: Use en dash for Lebwohl–Lasher

2018-09-17T21:54:50Z

Use en dash for Lebwohl–Lasher

Carl McBride: /* Isotropic-nematic transition */ Added a recent publication

2012-06-21T13:58:18Z

Isotropic-nematic transition: Added a recent publication

← Older revision		Revision as of 15:58, 21 June 2012
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	:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001 </math>		:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001 </math>

	See also the paper by Zhang ''et al.'' <ref>[http://dx.doi.org/10.1103/PhysRevLett.69.2803 Zhengping Zhang, Ole G. Mouritsen, and Martin J. Zuckermann, "Weak first-order orientational transition in the Lebwohl-Lasher model for liquid crystals", Physical Review Letters '''69''' pp. 2803-2806 (1992)]</ref>.		See also the paper by Zhang ''et al.'' <ref>[http://dx.doi.org/10.1103/PhysRevLett.69.2803 Zhengping Zhang, Ole G. Mouritsen, and Martin J. Zuckermann, "Weak first-order orientational transition in the Lebwohl-Lasher model for liquid crystals", Physical Review Letters '''69''' pp. 2803-2806 (1992)]</ref> and that of Shekhar et al. <ref>[http://dx.doi.org/10.1063/1.4722209 Raj Shekhar, Jonathan K. Whitmer, Rohit Malshe, J. A. Moreno-Razo, Tyler F. Roberts, and Juan J. de Pablo "Isotropic–nematic phase transition in the Lebwohl–Lasher model from density of states simulations", Journal of Chemical Physics '''136''' 234503 (2012)]</ref>.

	==Confined systems==		==Confined systems==

Noe: slight modification of the pair potential

2009-09-04T10:34:23Z

slight modification of the pair potential

← Older revision		Revision as of 12:34, 4 September 2009
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	The Lebwohl-Lasher model consists of a cubic lattice occupied by uniaxial [[Nematic phase\|nematogenic]] particles with the [[Intermolecular pair potential \| pair potential]]		The Lebwohl-Lasher model consists of a cubic lattice occupied by uniaxial [[Nematic phase\|nematogenic]] particles with the [[Intermolecular pair potential \| pair potential]]

	:<math>\Phi_{ij} = -\~~epsilon_{ij}~~ P_2 (\cos \beta_{ij}) </math>		:<math>\Phi_{ij} = -\epsilon P_2 (\cos \beta_{ij}) </math>

	where <math>\~~epsilon_{ij}~~ > 0</math>, <math>\beta_{ij}</math> is the angle between the axes of nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials \|Legendre polynomial]].		where <math>\epsilon > 0</math>, <math>\beta_{ij}</math> is the angle between the axes of nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials \|Legendre polynomial]].
	==Isotropic-nematic transition==		==Isotropic-nematic transition==
	Fabbri and Zannoni estimated the transition temperature <ref>[http://dx.doi.org/10.1080/00268978600101561 U. Fabbri and C. Zannoni "A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 '''58''' (1986)]</ref> via a [[Monte Carlo]] simulation:		Fabbri and Zannoni estimated the transition temperature <ref>[http://dx.doi.org/10.1080/00268978600101561 U. Fabbri and C. Zannoni "A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 '''58''' (1986)]</ref> via a [[Monte Carlo]] simulation:

Noe: /* Planar Lebwohl–Lasher model */

2009-04-17T18:21:14Z

Planar Lebwohl–Lasher model

← Older revision		Revision as of 20:21, 17 April 2009
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	==Planar Lebwohl–Lasher model ==		==Planar Lebwohl–Lasher model ==
	The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. The [[square lattice~~\|square lattice]]~~ is the usual choice for most of the simulation studies.		The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. The square lattice is the usual choice for most of the simulation studies.
	This system exhibits a continuous transition. The ascription of such a transition to the		This system exhibits a continuous transition. The ascription of such a transition to the
	[[Kosterlitz-Thouless transition\|Kosterlitz-Touless]] type is still under discussion		[[Kosterlitz-Thouless transition\|Kosterlitz-Touless]] type is still under discussion

Noe: /* Planar Lebwohl–Lasher model */ sq lattice

2009-04-17T18:20:05Z

Planar Lebwohl–Lasher model: sq lattice

← Older revision		Revision as of 20:20, 17 April 2009
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	==Planar Lebwohl–Lasher model ==		==Planar Lebwohl–Lasher model ==
	The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional.		The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional. The [[square lattice\|square lattice]] is the usual choice for most of the simulation studies.
	This system exhibits a continuous transition. The ascription of such a transition to the		This system exhibits a continuous transition. The ascription of such a transition to the
	[[Kosterlitz-Thouless transition\|Kosterlitz-Touless]] type is still under discussion		[[Kosterlitz-Thouless transition\|Kosterlitz-Touless]] type is still under discussion

Nice and Tidy: /* Confined systems */ Changed internal link. Nematogens cited previously.

2009-04-15T12:45:28Z

Confined systems: Changed internal link. Nematogens cited previously.

← Older revision		Revision as of 14:45, 15 April 2009
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	==Confined systems==		==Confined systems==
	The Lebwohl-Lasher model has been used to study the effect of confinement in the phase		The Lebwohl-Lasher model has been used to study the effect of [[Confined systems \|confinement]] in the phase
	behavior of ~~[[Nematic phase \|~~nematogens]] <ref>[http://dx.doi.org/10.1080/00268979300102251 Douglas J. Cleaver and Michael P. Allen, " Computer simulation of liquid crystal films", Molecular Physics '''80''' pp 253-276 (1993) ]</ref>		behavior of nematogens <ref>[http://dx.doi.org/10.1080/00268979300102251 Douglas J. Cleaver and Michael P. Allen, " Computer simulation of liquid crystal films", Molecular Physics '''80''' pp 253-276 (1993) ]</ref>

	==Planar Lebwohl–Lasher model ==		==Planar Lebwohl–Lasher model ==

Nice and Tidy: /* Confined systems */ Added an internal link.

2009-04-15T12:41:03Z

Confined systems: Added an internal link.

← Older revision		Revision as of 14:41, 15 April 2009
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	==Confined systems==		==Confined systems==
	The Lebwohl-Lasher model has been used to study the effect of confinement in the phase		The Lebwohl-Lasher model has been used to study the effect of confinement in the phase
	behavior of nematogens <ref>[http://dx.doi.org/10.1080/00268979300102251 Douglas J. Cleaver and Michael P. Allen, " Computer simulation of liquid crystal films", Molecular Physics '''80''', pp 253 - 276 (1993) ]</ref>		behavior of [[Nematic phase \|nematogens]] <ref>[http://dx.doi.org/10.1080/00268979300102251 Douglas J. Cleaver and Michael P. Allen, " Computer simulation of liquid crystal films", Molecular Physics '''80''' pp 253-276 (1993) ]</ref>

	==Planar Lebwohl–Lasher model ==		==Planar Lebwohl–Lasher model ==
	The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional.		The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional.

Noe: new reference added, new section (confinement)

2009-04-15T12:38:35Z

new reference added, new section (confinement)

← Older revision		Revision as of 14:38, 15 April 2009
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	See also the paper by Zhang ''et al.'' <ref>[http://dx.doi.org/10.1103/PhysRevLett.69.2803 Zhengping Zhang, Ole G. Mouritsen, and Martin J. Zuckermann, "Weak first-order orientational transition in the Lebwohl-Lasher model for liquid crystals", Physical Review Letters '''69''' pp. 2803-2806 (1992)]</ref>.		See also the paper by Zhang ''et al.'' <ref>[http://dx.doi.org/10.1103/PhysRevLett.69.2803 Zhengping Zhang, Ole G. Mouritsen, and Martin J. Zuckermann, "Weak first-order orientational transition in the Lebwohl-Lasher model for liquid crystals", Physical Review Letters '''69''' pp. 2803-2806 (1992)]</ref>.

			==Confined systems==
			The Lebwohl-Lasher model has been used to study the effect of confinement in the phase
			behavior of nematogens <ref>[http://dx.doi.org/10.1080/00268979300102251 Douglas J. Cleaver and Michael P. Allen, " Computer simulation of liquid crystal films", Molecular Physics '''80''', pp 253 - 276 (1993) ]</ref>
	==Planar Lebwohl–Lasher model ==		==Planar Lebwohl–Lasher model ==
	The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional.		The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional.

Nice and Tidy: /* Isotropic-nematic transition */ Added an internal link.

2009-04-15T11:05:43Z

Isotropic-nematic transition: Added an internal link.

← Older revision		Revision as of 13:05, 15 April 2009
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	where <math>\epsilon_{ij} > 0</math>, <math>\beta_{ij}</math> is the angle between the axes of nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials \|Legendre polynomial]].		where <math>\epsilon_{ij} > 0</math>, <math>\beta_{ij}</math> is the angle between the axes of nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials \|Legendre polynomial]].
	==Isotropic-nematic transition==		==Isotropic-nematic transition==
	Fabbri and Zannoni estimated the transition temperature <ref>[http://dx.doi.org/10.1080/00268978600101561 U. Fabbri and C. Zannoni "A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 '''58''' (1986)]</ref> ~~using~~ Monte Carlo simulation:		Fabbri and Zannoni estimated the transition temperature <ref>[http://dx.doi.org/10.1080/00268978600101561 U. Fabbri and C. Zannoni "A Monte Carlo investigation of the Lebwohl-Lasher lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 '''58''' (1986)]</ref> via a [[Monte Carlo]] simulation:

	:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1232 \pm 0.0006</math>		:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1232 \pm 0.0006</math>
Line 15:		Line 15:
	:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001 </math>		:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001 </math>

	See also the paper by Zhang ''et al.'' <ref>[http://dx.doi.org/10.1103/PhysRevLett.69.2803 Zhengping Zhang, Ole G. Mouritsen, and Martin J. Zuckermann, "Weak first-order orientational transition in the Lebwohl-Lasher model for liquid crystals", Physical Review Letters '''69''' pp. 2803-2806 (1992)]</ref>		See also the paper by Zhang ''et al.'' <ref>[http://dx.doi.org/10.1103/PhysRevLett.69.2803 Zhengping Zhang, Ole G. Mouritsen, and Martin J. Zuckermann, "Weak first-order orientational transition in the Lebwohl-Lasher model for liquid crystals", Physical Review Letters '''69''' pp. 2803-2806 (1992)]</ref>.

	==Planar Lebwohl–Lasher model ==		==Planar Lebwohl–Lasher model ==

Nice and Tidy: Trivial tidy.

2009-04-15T11:04:13Z

Trivial tidy.

← Older revision		Revision as of 13:04, 15 April 2009
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	:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1232 \pm 0.0006</math>		:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1232 \pm 0.0006</math>

	More recently N. V. Priezjev and Robert A. Pelcovits <ref>[http://dx.doi.org/10.1103/PhysRevE.63.062702 N. V. Priezjev and Robert A. Pelcovits ''Cluster Monte Carlo simulations of the nematic-isotropic transition'' Phys. Rev. E 63, 062702 (2001) [4 pages]] </ref> used a Monte Carlo [[cluster algorithms\|cluster algorithm]] and ~~got~~:		More recently N. V. Priezjev and Robert A. Pelcovits <ref>[http://dx.doi.org/10.1103/PhysRevE.63.062702 N. V. Priezjev and Robert A. Pelcovits ''Cluster Monte Carlo simulations of the nematic-isotropic transition'' Phys. Rev. E 63, 062702 (2001) [4 pages]] </ref> used a Monte Carlo [[cluster algorithms\|cluster algorithm]] and obtained:

	:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001 </math>		:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001 </math>
Line 20:		Line 20:
	The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional.		The planar Lebwohl-Lasher appears when the lattice considered is two-dimensional.
	This system exhibits a continuous transition. The ascription of such a transition to the		This system exhibits a continuous transition. The ascription of such a transition to the
	[[Kosterlitz-Thouless transition\|Kosterlitz-Touless]] type is still under discussion.		[[Kosterlitz-Thouless transition\|Kosterlitz-Touless]] type is still under discussion
	<ref>[http://dx.doi.org/10.1016/S0375-9601(03)00576-0 Enakshi Mondal and Soumen Kumar Roy "Finite size scaling in the planar Lebwohl–Lasher model", Physics Letters A '''312''' pp. 397-410 (2003)]</ref>		<ref>[http://dx.doi.org/10.1016/S0375-9601(03)00576-0 Enakshi Mondal and Soumen Kumar Roy "Finite size scaling in the planar Lebwohl–Lasher model", Physics Letters A '''312''' pp. 397-410 (2003)]</ref>
	<ref>[http://dx.doi.org/10.1016/0378-4371(88)90148-3 C. Chiccoli, P. Pasini, and C. Zannoni "A Monte Carlo investigation of the planar Lebwohl-Lasher lattice model", Physica A '''148''' pp. 298-311 (1988)]</ref>		<ref>[http://dx.doi.org/10.1016/0378-4371(88)90148-3 C. Chiccoli, P. Pasini, and C. Zannoni "A Monte Carlo investigation of the planar Lebwohl-Lasher lattice model", Physica A '''148''' pp. 298-311 (1988)]</ref>
	<ref> [http://link.aps.org/doi/10.1103/PhysRevB.46.662 H. Kunz, and G. Zumbach "Topological phase transition in a two-dimensional nematic n-vector model: A numerical study" Physical Review B '''46''', 662-673 (1992) ]</ref>		<ref> [http://link.aps.org/doi/10.1103/PhysRevB.46.662 H. Kunz, and G. Zumbach "Topological phase transition in a two-dimensional nematic n-vector model: A numerical study" Physical Review B '''46''', 662-673 (1992) ]</ref>
	<ref>[http://link.aps.org/doi/10.1103/PhysRevE.78.051706 Ricardo Paredes V., Ana Isabel Fariñas-Sánchez, and Robert Botet "No quasi-long-range order in a two-dimensional liquid crystal", Physical Review E 78, 051706 (2008)]</ref>		<ref>[http://link.aps.org/doi/10.1103/PhysRevE.78.051706 Ricardo Paredes V., Ana Isabel Fariñas-Sánchez, and Robert Botet "No quasi-long-range order in a two-dimensional liquid crystal", Physical Review E 78, 051706 (2008)]</ref>.

	==Lattice Gas Lebwohl-Lasher model==		==Lattice Gas Lebwohl-Lasher model==

← Older revision		Revision as of 23:54, 17 September 2018
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	The '''~~Lebwohl-Lasher~~ model''' is a lattice version of the [[Maier-Saupe mean field model]] of a [[Nematic phase \| nematic liquid crystal]]		The '''Lebwohl–Lasher model''' is a lattice version of the [[Maier-Saupe mean field model]] of a [[Nematic phase \| nematic liquid crystal]]
	<ref>[http://dx.doi.org/10.1103/PhysRevA.6.426 P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order—A Monte Carlo Calculation", Physical Review A '''6''' pp. 426 - 429 (1972)]</ref><ref>[http://dx.doi.org/10.1103/PhysRevA.7.2222.3 Erratum, Physical Review A '''7''' p. 2222 (1973)]</ref>.		<ref>[http://dx.doi.org/10.1103/PhysRevA.6.426 P. A. Lebwohl and G. Lasher "Nematic-Liquid-Crystal Order—A Monte Carlo Calculation", Physical Review A '''6''' pp. 426 - 429 (1972)]</ref><ref>[http://dx.doi.org/10.1103/PhysRevA.7.2222.3 Erratum, Physical Review A '''7''' p. 2222 (1973)]</ref>.
	The ~~Lebwohl-Lasher~~ model consists of a cubic lattice occupied by uniaxial [[Nematic phase\|nematogenic]] particles with the [[Intermolecular pair potential \| pair potential]]		The Lebwohl–Lasher model consists of a cubic lattice occupied by uniaxial [[Nematic phase\|nematogenic]] particles with the [[Intermolecular pair potential \| pair potential]]

	:<math>\Phi_{ij} = -\epsilon P_2 (\cos \beta_{ij}) </math>		:<math>\Phi_{ij} = -\epsilon P_2 (\cos \beta_{ij}) </math>
Line 7:		Line 7:
	where <math>\epsilon > 0</math>, <math>\beta_{ij}</math> is the angle between the axes of nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials \|Legendre polynomial]].		where <math>\epsilon > 0</math>, <math>\beta_{ij}</math> is the angle between the axes of nearest neighbour particles <math>i</math> and <math>j</math>, and <math>P_2</math> is a second order [[Legendre polynomials \|Legendre polynomial]].
	==Isotropic-nematic transition==		==Isotropic-nematic transition==
	Fabbri and Zannoni estimated the transition temperature <ref>[http://dx.doi.org/10.1080/00268978600101561 U. Fabbri and C. Zannoni "A Monte Carlo investigation of the ~~Lebwohl-Lasher~~ lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 '''58''' (1986)]</ref> via a [[Monte Carlo]] simulation:		Fabbri and Zannoni estimated the transition temperature <ref>[http://dx.doi.org/10.1080/00268978600101561 U. Fabbri and C. Zannoni "A Monte Carlo investigation of the Lebwohl–Lasher lattice model in the vicinity of its orientational phase transition", Molecular Physics pp. 763-788 '''58''' (1986)]</ref> via a [[Monte Carlo]] simulation:

	:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1232 \pm 0.0006</math>		:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1232 \pm 0.0006</math>
Line 15:		Line 15:
	:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001 </math>		:<math>T^*_{NI}= \frac{k_BT_{NI}}{\epsilon}=1.1225 \pm 0.0001 </math>

	See also the paper by Zhang ''et al.'' <ref>[http://dx.doi.org/10.1103/PhysRevLett.69.2803 Zhengping Zhang, Ole G. Mouritsen, and Martin J. Zuckermann, "Weak first-order orientational transition in the ~~Lebwohl-Lasher~~ model for liquid crystals", Physical Review Letters '''69''' pp. 2803-2806 (1992)]</ref> and that of Shekhar et al. <ref>[http://dx.doi.org/10.1063/1.4722209 Raj Shekhar, Jonathan K. Whitmer, Rohit Malshe, J. A. Moreno-Razo, Tyler F. Roberts, and Juan J. de Pablo "Isotropic–nematic phase transition in the Lebwohl–Lasher model from density of states simulations", Journal of Chemical Physics '''136''' 234503 (2012)]</ref>.		See also the paper by Zhang ''et al.'' <ref>[http://dx.doi.org/10.1103/PhysRevLett.69.2803 Zhengping Zhang, Ole G. Mouritsen, and Martin J. Zuckermann, "Weak first-order orientational transition in the Lebwohl–Lasher model for liquid crystals", Physical Review Letters '''69''' pp. 2803-2806 (1992)]</ref> and that of Shekhar et al. <ref>[http://dx.doi.org/10.1063/1.4722209 Raj Shekhar, Jonathan K. Whitmer, Rohit Malshe, J. A. Moreno-Razo, Tyler F. Roberts, and Juan J. de Pablo "Isotropic–nematic phase transition in the Lebwohl–Lasher model from density of states simulations", Journal of Chemical Physics '''136''' 234503 (2012)]</ref>.

	==Confined systems==		==Confined systems==
	The ~~Lebwohl-Lasher~~ model has been used to study the effect of [[Confined systems \|confinement]] in the phase		The Lebwohl–Lasher model has been used to study the effect of [[Confined systems \|confinement]] in the phase
	behavior of nematogens <ref>[http://dx.doi.org/10.1080/00268979300102251 Douglas J. Cleaver and Michael P. Allen, " Computer simulation of liquid crystal films", Molecular Physics '''80''' pp 253-276 (1993) ]</ref>		behavior of nematogens <ref>[http://dx.doi.org/10.1080/00268979300102251 Douglas J. Cleaver and Michael P. Allen, " Computer simulation of liquid crystal films", Molecular Physics '''80''' pp 253-276 (1993) ]</ref>

	==Planar Lebwohl–Lasher model ==		==Planar Lebwohl–Lasher model ==
	The planar ~~Lebwohl-Lasher~~ appears when the lattice considered is two-dimensional. The square lattice is the usual choice for most of the simulation studies.		The planar Lebwohl–Lasher appears when the lattice considered is two-dimensional. The square lattice is the usual choice for most of the simulation studies.
	This system exhibits a continuous transition. The ascription of such a transition to the		This system exhibits a continuous transition. The ascription of such a transition to the
	[[Kosterlitz-Thouless transition\|Kosterlitz-Touless]] type is still under discussion		[[Kosterlitz-Thouless transition\|Kosterlitz-Touless]] type is still under discussion
	<ref>[http://dx.doi.org/10.1016/S0375-9601(03)00576-0 Enakshi Mondal and Soumen Kumar Roy "Finite size scaling in the planar Lebwohl–Lasher model", Physics Letters A '''312''' pp. 397-410 (2003)]</ref>		<ref>[http://dx.doi.org/10.1016/S0375-9601(03)00576-0 Enakshi Mondal and Soumen Kumar Roy "Finite size scaling in the planar Lebwohl–Lasher model", Physics Letters A '''312''' pp. 397-410 (2003)]</ref>
	<ref>[http://dx.doi.org/10.1016/0378-4371(88)90148-3 C. Chiccoli, P. Pasini, and C. Zannoni "A Monte Carlo investigation of the planar ~~Lebwohl-Lasher~~ lattice model", Physica A '''148''' pp. 298-311 (1988)]</ref>		<ref>[http://dx.doi.org/10.1016/0378-4371(88)90148-3 C. Chiccoli, P. Pasini, and C. Zannoni "A Monte Carlo investigation of the planar Lebwohl–Lasher lattice model", Physica A '''148''' pp. 298-311 (1988)]</ref>
	<ref> [http://link.aps.org/doi/10.1103/PhysRevB.46.662 H. Kunz, and G. Zumbach "Topological phase transition in a two-dimensional nematic n-vector model: A numerical study" Physical Review B '''46''', 662-673 (1992) ]</ref>		<ref> [http://link.aps.org/doi/10.1103/PhysRevB.46.662 H. Kunz, and G. Zumbach "Topological phase transition in a two-dimensional nematic n-vector model: A numerical study" Physical Review B '''46''', 662-673 (1992) ]</ref>
	<ref>[http://link.aps.org/doi/10.1103/PhysRevE.78.051706 Ricardo Paredes V., Ana Isabel Fariñas-Sánchez, and Robert Botet "No quasi-long-range order in a two-dimensional liquid crystal", Physical Review E 78, 051706 (2008)]</ref>.		<ref>[http://link.aps.org/doi/10.1103/PhysRevE.78.051706 Ricardo Paredes V., Ana Isabel Fariñas-Sánchez, and Robert Botet "No quasi-long-range order in a two-dimensional liquid crystal", Physical Review E 78, 051706 (2008)]</ref>.

	==Lattice Gas ~~Lebwohl-Lasher~~ model==		==Lattice Gas Lebwohl–Lasher model==
	This model is the [[lattice gas]] version of the ~~Lebwohl-Lasher~~ model. In this case		This model is the [[lattice gas]] version of the Lebwohl–Lasher model. In this case
	the sites of the lattice can be occupied by particles or empty. The interaction		the sites of the lattice can be occupied by particles or empty. The interaction
	between nearest-neighbour particles is that of the ~~Lebwohl-Lasher~~ model.		between nearest-neighbour particles is that of the Lebwohl–Lasher model.
	This model has been studied in		This model has been studied in
	<ref>[http://dx.doi.org/10.1103/PhysRevE.64.051702 Martin A. Bates "Computer simulation study of the phase behavior of a nematogenic lattice-gas model", Physical Review E '''64''' 051702 (2001)]</ref>.		<ref>[http://dx.doi.org/10.1103/PhysRevE.64.051702 Martin A. Bates "Computer simulation study of the phase behavior of a nematogenic lattice-gas model", Physical Review E '''64''' 051702 (2001)]</ref>.