Universal, finite temperature, crossover functions of the quantum transition in the Ising chain in a transverse field

TL;DR

This paper derives universal finite-temperature crossover functions for static and dynamic correlators near the quantum phase transition in the Ising chain in a transverse field, connecting quantum and classical dynamics.

Contribution

It introduces new universal crossover functions for static and dynamic correlators, using analytic continuation and a mapping to classical Glauber dynamics.

Findings

Derived static crossover functions from lattice computations

Obtained dynamic crossover functions in the renormalized classical region

Established a mapping between quantum dynamics and classical Glauber dynamics

Abstract

We consider finite temperature properties of the Ising chain in a transverse field in the vicinity of its zero temperature, second order quantum phase transition. New universal crossover functions for static and dynamic correlators of the ``spin'' operator are obtained. The static results follow from an early lattice computation of McCoy, and a method of analytic continuation in the space of coupling constants. The dynamic results are in the ``renormalized classical'' region and follow from a proposed mapping of the quantum dynamics to the Glauber dynamics of a classical Ising chain.