Tunneling and Energy Splitting in Ising Models

TL;DR

This paper measures the energy splitting in finite Ising models using Monte Carlo simulations, validating theoretical predictions in 2D and 4D, and demonstrating the reliability of extracting energy splittings in finite lattice systems.

Contribution

It provides a reliable Monte Carlo method to measure energy splitting in Ising models and compares results with theoretical predictions, supporting the dilute instanton gas approximation in four dimensions.

Findings

Energy splitting can be reliably extracted from Monte Carlo data.

Numerical results agree with the dilute instanton gas approximation in 4D.

Exact solutions in 2D validate the measurement approach.

Abstract

The energy splitting $E_{0a}$ in two and four dimensional Ising models is measured in a cylindrical geometry on finite lattices. By comparing to exact results in the two dimensional Ising model we demonstrate that $E_{0a}$ can be extracted very reliably from Monte Carlo calculations in practice. In four dimensions we compare the measured $E_{0a}$ with two different theoretical predictions on the finite size behavior of the energy splitting. We find that our numerical data are in favor of the predictions based on the semiclassical dilute instanton gas approximation.