Breakdown of replica analyticity in the one-dimensional axis model

Abstract

We consider a random-bond one-dimensional m-component axis model, which has a transition for m<1. We solve the model exactly with and without using the replica trick. Below the transition, the exact zeros of the partition function 〈$Z_N^n$〉 move towards the positive real n axis in the thermodynamic limit indicating the breakdown of analytic continuation: We cannot approach the n=0 point once the thermodynamic limit is taken. We also show that we cannot interchange the thermodynamic and the replica limits below the transition.