Sine-square deformation applied to classical Ising models

TL;DR

This paper explores the application of sine-square deformation (SSD) to classical Ising models, revealing that SSD creates an extended ensemble with local effective temperatures, enabling accurate reproduction of uniform system properties.

Contribution

It introduces the novel application of SSD to classical Ising models and demonstrates its effectiveness in reproducing uniform system properties through analytical and simulation methods.

Findings

SSD creates an extended canonical ensemble with local effective temperatures.

A single calculation at fixed temperature yields properties of various temperatures.

SSD accurately reproduces properties of the uniform classical Ising system.

Abstract

Sine-square deformation (SSD) is a treatment proposed in quantum systems, which spatially modifies a Hamiltonian, gradually decreasing the local energy scale from the center of the system toward the edges by a sine-squared envelope function. It is known to serve as a good boundary condition as well as to provide physical quantities reproducing those of the infinite-size systems. We apply the SSD to one- and two-dimensional classical Ising models. Based on the analytical calculations and Monte Carlo simulations, we find that the classical SSD system is regarded as an extended canonical ensemble of a local subsystem each characterized by its own effective temperature. This effective temperature is defined by normalizing the system temperature by the deformed local energy scale. A single calculation for a fixed system temperature provides a set of physical quantities of various temperatures that quantitatively reproduce well those of the uniform system.