Regge theory and statistical mechanics

Abstract

An interesting connection between the Regge theory of scattering, the Veneziano amplitude, the Lee-Yang theorems in statistical mechanics and nonextensive Renyi entropy is addressed. In this scheme the standard entropy and the Renyi entropy appear to be different limits of a unique mathematical object. This framework sheds light on the physical origin of nonextensivity. A non trivial application to spin glass theory is shortly outlined.

Kallen–Lehman approach to 3D Ising model

“…where C (2) is the two dimensional contribution and C (3) the three dimensional one. A trivial but cumbersome computation gives…”

“…It is worth to note that E (1) , E (2) and E (3) diverge when K ν approaches to 1. However, in the first two terms…”

Minimal duality breaking in the Kallen–Lehman approach to 3D Ising model: A numerical test

“…It has been recently proposed [3] to use in statistical mechanics the powerful tools of Regge theory [4,5] which have been so fruitful in the study of the strong interactions leading to the formulation of the dual models [6] (two detailed reviews are [7] and [8]). It has been argued in [9] that such ideas may be useful in dealing with the 3D Ising model.…”

Duality and Fisher zeros in the two-dimensional Potts model on a square lattice

“…Following the point of view of the phenomenological Regge theory of scattering (see [9] and [10]; two detailed reviews are [11] and [12]), a reasonable analytic form for the free energy in terms of one free parameter will be derived. In the present case it plays the role of Regge's trajectories in high energy physics since it parametrises some analytical features of the Potts model such as its duality properties and the Fisher zeros, in an analogue way as the Regge trajectories encode the non-perturbative duality properties of scattering amplitudes, as was first observed in [13]. This can be done by requiring that the sought analytic expression for the free energy of the 2D Potts model should be compatible (in a suitable sense explained in the next sections) with the proposal made in [14], [15], [16] for the free energy of the three dimensional Ising model.…”