Exact field-driven interface dynamics in the two-dimensional stochastic Ising model with helicoidal boundary conditions

TL;DR

This paper analyzes the exact dynamics of interfaces in a 2D stochastic Ising model with helicoidal boundary conditions, revealing solvable quantum Hamiltonians and KPZ universality class behavior at low temperatures and fields.

Contribution

It introduces an exactly solvable quantum Hamiltonian framework for the interface dynamics in the 2D stochastic Ising model with helicoidal boundary conditions, connecting to KPZ universality.

Findings

Interface dynamics described by an exactly solvable high-spin asymmetric quantum Hamiltonian.

Critical interface fluctuations belong to the KPZ universality class.

A family of RSOS interface models can be characterized by exactly solvable XXZ-type Hamiltonians.

Abstract

We investigate the interface dynamics of the two-dimensional stochastic Ising model in an external field under helicoidal boundary conditions. At sufficiently low temperatures and fields, the dynamics of the interface is described by an exactly solvable high-spin asymmetric quantum Hamiltonian that is the infinitesimal generator of the zero range process. Generally, the critical dynamics of the interface fluctuations is in the Kardar-Parisi-Zhang universality class of critical behavior. We remark that a whole family of RSOS interface models similar to the Ising interface model investigated here can be described by exactly solvable restricted high-spin quantum XXZ-type Hamiltonians.