Finding and classifying an infinite number of cases of the marginal phase transition in one-dimensional Ising models

TL;DR

This paper discovers and classifies an infinite number of marginal phase transition cases in a one-dimensional Ising model with geometrical frustration, revealing new behaviors and potential applications in simulating complex phase phenomena.

Contribution

It introduces a new mathematical framework that identifies and categorizes numerous MPT cases, expanding understanding of phase transitions in 1D systems.

Findings

Infinite MPT cases classified with tunable behaviors

Reentrant phase transitions and dome-shaped transition temperatures identified

Potential for building MPT-based Ising Machines for complex system simulation

Abstract

One-dimensional systems---ranging from travelling light to circuit cables and from DNA to superstrings---are ubiquitous and critically important to the human knowledge of the universe. However, our engagement with one-dimensional systems in the research and education of spontaneous phase transitions, the phenomena wherein materials can change rapidly between different phases (e.g., gas, liquid, solid, etc.) on their own, has not been largely exercised, since it was proven that one-dimensional systems do not contain phase transitions in the textbook Ising model almost 100 years ago [1] and its quantum counterpart, the Heisenberg model, over 50 years ago [2]. Recently, a spontaneous marginal phase transition (MPT) was discovered in a one-dimensional Ising model containing strong geometrical frustration [3]. Here, by exploring the symmetry of the new mathematical structure underlying the MPT, I report the finding and classification of an infinite number of MPT cases---with highly tunable intriguing behaviors like phase reentrance, the dome shape of transition temperature, pairing, and gauge freedom. These discoveries reveal the possibility of building the MPT-based one-dimensional Ising Machine that can be used to simulate the complex phenomena of phase competition in strongly correlated systems and provide insights with its unambiguous exact solutions. They also form a rich playground for exploring unconventional phase transitions in one-dimensional Heisenberg models.