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Lattice models of 2D (and 3D) liquid crystal:

Self-Assembled Rigid Rods: (Polydispersive, Center of monomers are on the lattice.)
1507.04590: Nikolai I. Lebovka, Yuri Yu. Tarasevich, Dmitri O. Dubinin, Valeri V. Laptev, Nikolai V. Vygornitskii, "Jamming and percolation in generalized models of random sequential adsorption of linear $k$-mers on a square lattice"
1410.0307: J. F. Stilck, R. Rajesh, "Polydispersed rods on the square lattice"
1303.0922: L. G. Lopez, D. H. Linares, A. J. Ramirez-Pastor, D. A. Stariolo, S. A. Cannas, "Critical behavior of self-assembled rigid rods on two-dimensional lattices: Bethe-Peierls approximation and Monte Carlo simulations"
1211.0896: L. G. Lopez, A. J. Ramirez-Pastor, "Adsorption of Self-Assembled Rigid Rods on Two-Dimensional Lattices"
1207.7313: N. G. Almarza, J. M. Tavares, M. M. Telo da Gama, "The nature of the ordered phase of the confined self-assembled rigid rod model"
1205.0902: N. G. Almarza, J. M. Tavares, M. M. Telo da Gama, "Reply to Comment on Effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods"
1205.0274: L. G. Lopez, D. H. Linares, A. J. Ramirez-Pastor, "Comment on: Effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods"
1010.3937: N.G. Almarza, J. M. Tavares, M. M. Telo da Gama, "The effect of polydispersity on the ordering transition of adsorbed self-assembled rigid rods"
1010.2519: L. G. Lopez, D. H. Linares, A. J. Ramirez-Pastor, S. A. Cannas, "Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations"
1010.2517: L. G. Lopez, D. H. Linares, A. J. Ramirez-Pastor, "Critical behavior of self-assembled rigid rods on triangular and honeycomb lattices"
0904.0269: L. G. Lopez, D. H. Linares, A. J. Ramirez-Pastor, "Critical exponents and universality for the isotropic-nematic phase transition in a system of self-assembled rigid rods on a lattice"
0902.PRE: J. M. Tavares, B. Holder, and M. M. Telo da Gama, "Structure and phase diagram of self-assembled rigid rods: Equilibrium polydispersity and nematic ordering in two dimensions"

Rigid Rods: (Fixed Length, Monomers are on the Lattice/Face/Plaquette.)
2002.00875: Christophe Chatelain, Andrej Gendiar, "Absence of logarithmic divergence of the entanglement entropies at the phase transitions of a 2D classical hard rod model"
1706.05185: A. Gschwind, M. Klopotek, Y. Ai, M. Oettel, "The isotropic--nematic transition for hard rods on a three--dimensional (3D) cubic lattice"
1705.10531: N. Vigneshwar, Deepak Dhar, R. Rajesh, "Different phases of a system of hard rods on three dimensional cubic lattice"
1601.02198: Trisha Nath, Deepak Dhar, R. Rajesh, "Stability of columnar order in assemblies of hard rectangles or squares"
1510.07375: Joyjit Kundu, Jurgen F. Stilck, R. Rajesh, "Phase diagram of a bidispersed hard rod lattice gas in two dimensions"
1412.7267: Yuri Yu. Tarasevich, Valeri V. Laptev, Nikolai V. Vygornitskii, Nikolai I. Lebovka, "Impact of defects on percolation in random sequential adsorption of linear k-mers on square lattice"
1408.4943: Kabir Ramola, Kedar Damle, Deepak Dhar, "Columnar order and Ashkin-Teller criticality in mixtures of hard-squares and dimers"
1401.5590: Joyjit Kundu, R. Rajesh, "Phase transitions in a system of hard rectangles on the square lattice"
1211.2536: Joyjit Kundu, R. Rajesh, Deepak Dhar, Jurgen F. Stilck, "The nematic-disordered phase transition in systems of long rigid rods on two dimensional lattices"
1204.4484: Kabir Ramola, Deepak Dhar, "High-Activity Perturbation Expansion for the Hard Square Lattice Gas"
1106.2368: Jeferson J. Arenzon, Deepak Dhar, Ronald Dickman, "Glassy dynamics and hysteresis in a linear system of orientable hard rods"
0804.3614: D. A. Matoz-Fernandez, D. H. Linares, A.J. Ramirez-Pastor, "Critical behavior of long straight rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations"
0712.4361: D. H. Linares, F. Roma, A. J. Ramirez-Pastor, "Entropy-driven phase transition in a system of long rods on a square lattice"
0708.0395: D. A. Matoz-Fernandez, D. H. Linares, A. J. Ramirez-Pastor, "Determination of the Critical Exponents for the Isotropic-Nematic Phase Transition in a System of Long Rods on Two-dimensional Lattices: Universality of the Transition"
cond-mat/0611361: Anandamohan Ghosh, Deepak Dhar, "On the orientational ordering of long rods on a lattice"
cond-mat/0606391: P. M. Pasinetti, F. Roma, J. L. Riccardo, A. J. Ramirez-Pastor, "Critical behavior of repulsive linear $k$-mers on triangular lattices"

Vertex Model: (Polydispersive, Center of monomers are on the bond/link.)
cond-mat/0012490: Hiroshi Takasaki, Tomotoshi Nishino, Yasuhiro Hieida, "Phase Diagram of a 2D Vertex Model"

Random Sequential Adsorption: (of linear k-mers.)
1109.3271: Nikolai I. Lebovka, Natalia N. Karmazina, Yuri Yu. Tarasevich, Valeri V. Laptev, "Random sequential adsorption of partially oriented linear k-mers on square lattice"

Others (Experiment, etc.): (.... Chozen by chance ....)
1810.06800: M. G. Slutskii, L. Yu. Barash, Yu. Yu. Tarasevich, "Percolation and jamming of random sequential adsorption samples of large linear k-mers on a square lattice"
1712.02301: Dipanjan Mandal, Trisha Nath, R. Rajesh, "Phase transitions in a system of hard Y-shaped particles on the triangular lattice"
1702.02332: Dipanjan Mandal, Trisha Nath, R. Rajesh, "Estimating the Critical Parameters of the Hard Square Lattice Gas Model"
1608.02924: Rogerio Costa Hart, Fabio David Alves Aarao Reis, "Random sequential adsorption of polydisperse mixtures on lattices"
1607.06851: Yuri Martinez-Raton, Miguel Gonzalez-Pinto, Enrique Velasco, "Biaxial nematic phase stability and demixing behaviour in monolayers of rod-plate mixtures"
cond-mat/0406175: Kirstin Purdy, Szabolcs Varga, Amparo Galindo, George Jackson, Seth Fraden, "Nematic phase transitions in mixtures of thin and thick colloidal rods"

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