The Ising model coupled to 2d orders

Multiple Ising Spins Coupled to 2d Quantum Gravity

We study a model in which p independent Ising spins are coupled to 2d quantum gravity (in the form of dynamical planar φ graphs). Consideration is given to the p→∞ limit in which the partition function becomes dominated by certain graphs; we identify most of these graphs. A truncated model is solved exactly providing information about the behaviour of the full model in the limit β → 0. Finally,...

A Two Term Truncation of the Multiple Ising Model Coupled to 2d Gravity

We consider a model of p independent Ising spins on a dynamical planar φ graph. Truncating the free energy to two terms yields an exactly solvable model that has a third order phase transition from a pure gravity region (γstr = −1/2) to a tree-like region (γstr = 1/2), with γstr = 1/3 on the critical line. We are able to make an order of magnitude estimate of the value of p above which there ex...

The solution of the 2D Ising model

Correlation Functions in the Multiple Ising Model Coupled to Gravity

The model of p Ising spins coupled to 2d gravity, in the form of a sum over planar φ graphs, is studied and in particular the two-point and spin-spin correlation functions are considered. We first solve a toy model in which only a partial summation over spin configurations is performed and, using a modified geodesic distance, various correlation functions are determined. The two-point function ...

The Surface Tension near Criticality of the 2d-ising Model

For the two dimensional Ising model, we construct the adequate surface tension near criticality. The latter quantity has been shown [9] to play a central role in the study of phase coexistence in a joint limit where the temperature approaches the critical point from below and simultaneously the size of the system increases fast enough.