6 papers
A new upper bound on the dimer constant of
Qidong He
We prove that the dimer constant of the cubic lattice is bounded above by , improving the previous best upper bound of obtained by Lundow (2001) using the tran…
Rigorous bound on the aspect ratio for the formation of a nematic phase in hard rod and hard rectangle systems on
Qidong He
We prove the existence of a nematic phase in a model of hard rectangles on the square lattice with two allowed orientations and a large aspect ratio . The proof…
Unified criteria for crystallization in hard-core lattice systems with applications to polyomino fluids and multi-component mixtures
Qidong He
We present a unified extension of two sets of criteria for high-fugacity crystallization in hard-core lattice systems developed previously by Jauslin, Lebowitz, and the author. Our…
Extended regime of nematic order in an interacting monomer-dimer model of Heilmann and Lieb
Qidong He
We revisit a two-dimensional model of liquid crystals introduced by Heilmann and Lieb (1979), which consists of a system of dimers on the square lattice at chemical potential ,…
Liquid-vapor transition in a model of a continuum particle system with finite-range modified Kac pair potential
Qidong He, Ian Jauslin, Joel Lebowitz +1
We prove the existence of a phase transition in dimension in a continuum particle system interacting with a pair potential containing a modified attractive Kac potential of r…
Upper bounds for the connective constant of weighted self-avoiding walks
Qidong He
Building on a work by Alm, we consider a model of weighted self-avoiding walks on a lattice and develop a method for computing upper bounds on the corresponding weighted connective…