Columnar-disorder phase boundary in a mixture of hard squares and dimers

Abstract

A mixture of hard squares, dimers, and vacancies on a square lattice is known to undergo a transition from a low-density disordered phase to a high-density columnar ordered phase. Along the fully packed square-dimer line, the system undergoes a Kosterliz-Thouless-type transition to a phase with power law correlations. We estimate the phase boundary separating the ordered and disordered phases by calculating the interfacial tension between two differently ordered phases within two different approximation schemes. The analytically obtained phase boundary is in good agreement with Monte Carlo simulations.

Phases of the hard-plate lattice gas on a three-dimensional cubic lattice

“…A two dimensional section of the system of hard plates corresponds to a problem of hard squares and dimers. This model, when the activities of dimers and squares can be varied independently, has a very rich phase diagram including two lines of critical points meeting at a point [29,30]. Thus, one can expect that if the activities of the three kinds of plates in three dimensions can be independently varied, then a very rich phase diagram can be expected, especially at full packing, where regions of power-law correlated phases should exist.…”

“…Parallel to the study of models in the continuum, models of hard-core particles on lattices, known as hard core lattice gases (HCLGs) have also been studied. In literature, many different geometrical shapes have been studied in two dimensional lattices, which include triangles [17], squares [18][19][20][21][22][23], dimers [24][25][26][27], Y-shaped particles [28], mixture of squares and dimers [29,30], rods [31,32], rectangles [33][34][35][36], discretised discs or the k-NN model [37][38][39][40][41], hexagons [42], etc., the last being the only exactly solvable model. A variety of different ordered phases may be observed including crystalline, columnar or striped, nematic, power-law correlated phases, etc.…”

Alternative characterization of the nematic transition in deposition of rods on two-dimensional lattices

“…Other examples, corresponding to phase transitions in systems of hard particles of different shapes include triangles [2], squares [3][4][5][6][7][8][9], dimers [10][11][12][13], mixtures of squares and dimers [14,15], Y-shaped particles [16][17][18], tetrominoes [19,20], rods [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], rectangles [26,[37][38][39], disks [40,41], and hexagons [42]. Experimental realizations of such systems include tobacco mosaic virus [43,44], liquid crystals [45], f d virus [46][47][48], silica colloids [49,…”

Entropy of fully packed hard rigid rods on $d$-dimensional hyper-cubic lattices

“…An analytical exact solution has been possible only for the case of hard hexagons so far [21]. Phase transitions have also been studied in mixtures of different shapes, for example squares and dimers [17,40], rods of different lengths [41,42], polydispersed spheres [43], etc. For square-dimers, it was shown that the critical exponents of the order-disorder transition depends continuously on the relative concentration of the components.…”