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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 obtained:
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:


:<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>
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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==
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