Classical phase transitions in a one-dimensional short-range spin model induced by entropy depletion or complex fields

TL;DR

This paper demonstrates that entropy depletion and complex fields can induce classical phase transitions in one-dimensional short-range spin models, challenging traditional no-go theorems and expanding understanding of phase transition mechanisms.

Contribution

It introduces novel methods to achieve phase transitions in 1D systems by entropy manipulation and complex fields, beyond long-range interaction strategies.

Findings

Entropy depletion via invisible states induces phase transitions.

Complex fields can trigger phase transitions in 1D models.

The approach offers new avenues for physical realization of such systems.

Abstract

Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the Potts model with invisible states.Because spins in such a state do not interact with their surroundings, they contribute to the entropy but not the interaction energy of the system. Reducing the number of invisible states to a negative value decreases the entropy by an amount sufficient to induce a positive-temperature classical phase transition. This approach is complementary to the long-range interaction mechanism. Alternatively, subjecting positive numbers of invisible states to imaginary or complex fields can trigger such a phase transition. We also discuss potential physical realisability of such systems.