Analytic properties of the free energy: the tricritical Ising model

TL;DR

This paper studies the analytic structure of the free energy in the tricritical Ising model under complex magnetic fields, revealing edge singularities and complex conjugate spinodal points through combined analytic and numerical methods.

Contribution

It introduces a nonperturbative approach to analyze the free energy's analytic properties in non-integrable field theories, identifying novel singularities.

Findings

Confirmed existence of Lee-Yang type edge singularities.

Discovered two branching points resembling complex conjugate spinodal singularities.

Provided nonperturbative data using truncated conformal space techniques.

Abstract

We investigate the tricritical Ising model in complex magnetic field in order to characterize the analytic structure of its free energy. By supplementing analytic methods with the truncation of conformal space technique we obtain nonperturbative data even if the field theories we consider are not integrable. The existence of edge singularities analogous to the Lee-Yang points in the Ising field theory is confirmed. A surprising result, due to the conformal dimensions of the operators involved, is the appearance of two branching points which seems appealing to identify with a pair of complex conjugate spinodal singularities.