Low--Temperature Series for Renormalized Operators: the Ferromagnetic Square--Lattice Ising Model.

TL;DR

This paper introduces a method to compute low-temperature series for renormalized operators in the 2D Ising model, analyzing the properties of truncated Hamiltonians near the phase transition.

Contribution

It presents a novel approach for calculating low-temperature series for renormalized operators and examines their behavior in truncated Hamiltonians at phase transitions.

Findings

Truncated Hamiltonians depend on the approach to the phase transition line.

Renormalization Group transformations are multi-valued and discontinuous at the first-order transition.

The method provides insights into the properties of the Ising model at low temperatures.

Abstract

A method for computing low--temperature series for renormalized operators in the two--dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation and decimation for $2 \times 2$ blocks depend on the how we approach the first--order phase--transition line. These Renormalization Group transformations are multi--valued and discontinuous at this first--order transition line when restricted to some finite--dimensional interaction space.