A Fully Magnetizing Phase Transition

TL;DR

This paper investigates the Farey spin chain, revealing a sharp phase transition at a critical temperature where magnetization abruptly changes from zero to full magnetization, using polymer model techniques.

Contribution

It introduces a novel analysis of the Farey spin chain's phase transition employing polymer model methods to rigorously demonstrate the magnetization jump.

Findings

Magnetization jumps from zero to one at T_c=1/2

The phase transition is sharp and discontinuous

Polymer model techniques effectively analyze the spin system

Abstract

We analyze the Farey spin chain, a one dimensional spin system with effective interaction decaying like the squared inverse distance. Using a polymer model technique, we show that when the temperature is decreased below the (single) critical temperature T_c=1/2, the magnetization jumps from zero to one.