# Chiral Magnetic Effect in a Lattice Model

## TL;DR

This paper investigates the chiral magnetic effect using lattice regularization, finding it vanishes at nonzero temperature in the continuum limit but persists at finite lattice size, with small numerical values compared to full QCD simulations.

## Contribution

It provides an analytical study of the CME on a lattice with Wilson fermions, highlighting temperature dependence and finite size effects, and compares results with full QCD simulations.

## Key findings

- CME current vanishes at nonzero temperature in the continuum limit
- CME current is nonvanishing at finite lattice size and nonzero temperature
- Numerical CME coefficient is much smaller than in full QCD simulations

## Abstract

We study analytically the one-loop contribution to the Chiral Magnetic Effect(CME) using lattice regularization with a Wilson fermion field. In the continuum limit, we find that the chiral magnetic current vanishes at nonzero temperature but emerges at zero temperature consistent with that found by Pauli-Villas regularization. For finite lattice size, however, the chiral magnetic current is nonvanishing at nonzero temperature. But the numerical vaule of the coefficient of CME current is very small compared with that extracted from the full QCD simulation for the same lattice parameters. The possibility of higher order corrections from QCD dynamics is also assessed.