Ising model: Elementary excitation and nonsingular heat capacity at critical temperature

TL;DR

This paper introduces a new parameter vector to describe spin correlations in the Ising model, revealing harmonic motions that explain the nonsingular heat capacity at the critical temperature through block-spin phonons.

Contribution

It proposes a novel parameter vector q to analyze spin fluctuations and identifies harmonic motions and block-spin phonons as key to understanding heat capacity behavior.

Findings

Identification of a new parameter vector q for spin correlations

Discovery of harmonic motions and block-spin phonons in the Ising model

Explanation of nonsingular heat capacity at critical temperature

Abstract

We find a new parameter vector q to describe spin correlations and fluctuation characteristics. The conservation of scalar q indicates there are simple harmonic motions of q, and the motion quantum is called block-spin phonon like the phonon in a crystal, resulting in nonsingular heat capacity at T . The harmonic motions show there are hierarchies and symmetries of fluctuations, and the soft modes lead to the interactions of block-spin phonons of different frequencies.