Fields, particles and universality in two dimensions

TL;DR

This paper explores how field theory can precisely determine universal properties in two-dimensional statistical mechanics, covering critical exponents, off-critical systems, and various phenomena like magnetism and percolation.

Contribution

It provides a compact derivation of critical exponents and extends analysis to off-critical systems with boundaries, enhancing understanding of universality in 2D models.

Findings

Derived critical exponents for main universality classes

Analyzed off-critical systems on plane and with boundaries

Discussed applications to magnetism, percolation, and interfaces

Abstract

We discuss the use of field theory for the exact determination of universal properties in two-dimensional statistical mechanics. After a compact derivation of critical exponents of main universality classes, we turn to the off-critical case, considering systems both on the whole plane and in presence of boundaries. The topics we discuss include magnetism, percolation, phase separation, interfaces, wetting.