Ising Field Theory on a Pseudosphere

TL;DR

This paper explores the Ising field theory on a pseudosphere, deriving form factors and differential equations for correlation functions, and solving a connection problem related to Painleve VI, with implications for thermodynamics.

Contribution

It introduces a novel analysis of the Ising model on a pseudosphere, including explicit form factors and solutions to complex differential equations.

Findings

Derived form factors of spin fields.

Solved the connection problem for Painleve VI.

Discussed thermodynamic properties.

Abstract

We show how the symmetries of the Ising field theory on a pseudosphere can be exploited to derive the form factors of the spin fields as well as the non-linear differential equations satisfied by the corresponding two-point correlation functions. The latter are studied in detail and, in particular, we present a solution to the so-called connection problem relating two of the singular points of the associated Painleve VI equation. A brief discussion of the thermodynamic properties is also presented.