Two-dimensional Quantum Field Models (with applications to Statistical Mechanics)

TL;DR

This paper explores the two-dimensional Thirring model, illustrating key quantum field theory concepts and its relevance to statistical mechanics, especially in understanding critical phenomena in lattice systems.

Contribution

It provides an in-depth analysis of the Thirring model, highlighting its exact solvability, anomalous dimensions, and role in connecting quantum field theory with statistical mechanics.

Findings

Demonstrates the exact solvability of the Thirring model

Shows the anomalous dimensions of fields in the model

Links the model to critical exponents in statistical mechanics

Abstract

Two dimensional toy models display, in a gentler setting, manysalient aspects of Quantum Field Theory. Here I discuss a concrete two dimensional case, the Thirring model, which illustrates several important concepts of this theory: the anomalous dimension of the fields; the exact solvability; the anomalies of the Ward-Takahashi identities. Besides, I give a glimpse of the decisive role that this model plays in the study of an apparently unrelated topic: correlation critical exponents of two dimensional lattice systems of Statistical Mechanics.