Computational Study of a Multistep Height Model

TL;DR

This paper investigates a multistep height model using a worm algorithm, revealing how relaxing height step constraints affects critical behavior and linking results to Coulomb gas and O(n) loop models.

Contribution

It introduces a computational approach to study a multistep height model and establishes a connection between critical exponents and Coulomb gas coupling.

Findings

Critical temperature and exponents vary with height step parameter.

Exponents map to O(n) loop model on honeycomb lattice.

Model reduces to 2D Ising in a specific limit.

Abstract

An equilibrium random surface multistep height model proposed in [Abraham and Newman, EPL, 86, 16002 (2009)] is studied using a variant of the worm algorithm. In one limit, the model reduces to the two-dimensional Ising model in the height representation. When the Ising model constraint of single height steps is relaxed, the critical temperature and critical exponents are continuously varying functions of the parameter controlling height steps larger than one. Numerical estimates of the critical exponents can be mapped via a single parameter-- the Coulomb gas coupling-- to the exponents of the O(n) loop model on the honeycomb lattice with n <= 1.