Real time correlations at finite Temperature for the Ising model

TL;DR

This paper introduces a method to measure real-time evolution at finite temperature in the 1+1 Ising model, enabling the study of spatial correlations and relaxation times, with implications for more complex quantum field theories.

Contribution

It applies a new measurement scheme to the 1+1 Ising model to analyze real-time correlations at finite temperature, paving the way for studying more complex theories.

Findings

Computed spin correlation probabilities over time at finite T

Identified fixed points for the continuum real-time limit

Demonstrated the method's applicability to simple field theories

Abstract

After having developed a method that measures real time evolution of quantum systems at a finite temperature, we present here the simplest field theory where this scheme can be applied to, namely the 1+1 Ising model. We will compute the probability that if a given spin is up, some other spin will be up after a time $t$, the whole system being at temperature $T$. We can thus study spatial correlations and relaxation times at finite $T$. The fixed points that enable the continuum real time limit can be easily found for this model. The ultimate aim is to get to understand real time evolution in more complicated field theories, with quantum effects such as tunneling at finite temperature.