Random Walk Construction of Spinor Fields on Three Dimensional Lattice

TL;DR

This paper constructs Euclidean invariant spinor field theories on a 3D lattice using a random walk approach, calculates key physical quantities, and explores their continuum limit and universality across different lattice structures.

Contribution

It introduces a novel random walk method with a spin factor for constructing lattice spinor fields and provides exact calculations of free energy and correlation functions.

Findings

Critical exponents do not satisfy hyper-scaling relations.

Exact free energy and correlation functions are obtained.

Universality is confirmed across different lattice types.

Abstract

Euclidean invariant Klein-Gordon, Dirac and massive Chern-Simons field theories are constructed in terms of a random walk with a spin factor on a three dimensional lattice. We exactly calculate the free energy and the correlation functions which allow us to obtain the critical diffusion constant and associated critical exponents. It is pointed out that these critical exponents do not satisfy the hyper-scaling relation but the scaling inequalities. We take the continuum limit of this theory on the basis of these analyses. We check the universality of obtained results on other lattice structure such as triclinic lattice and body centered lattice.