title: Asymptotic behavior of the isotropic-nematic and nematic-columnar phase boundaries for the system of hard rectangles on a square lattice.
abstract: A system of hard rectangles of size m×mk on a square lattice undergoes three entropy-driven phase transitions with increasing density for large-enough aspect ratio k: first from a low-density isotropic to an intermediate-density nematic phase, second from the nematic to a columnar phase, and third from the columnar to a high-density sublattice phase. In this paper we show, from extensive Monte Carlo simulations of systems with m=1,2, and 3, that the transition density for the isotropic-nematic transition is ≈A(1)/k when k≫1, where A(1) is independent of m. We estimate A(1)=4.80±0.05. Within a Bethe approximation and virial expansion truncated at the second virial coefficient, we obtain A(1)=2. The critical density for the nematic-columnar transition when m=2 is numerically shown to tend to a value less than the full packing density as k(-1) when k→∞. We find that the critical Binder cumulant for this transition is nonuniversal and decreases as k(-1) for k≫1. However, the transition is shown to be in the Ising universality class.
authors: The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India.
authors: Joyjit
authors: J
authors: Kundu
authors: The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India.
authors: R
authors: R
authors: Rajesh