A paradigm of spontaneous marginal phase transition at finite temperature in one-dimensional ladder Ising models

TL;DR

This paper introduces the concept of marginal phase transition (MPT) in one-dimensional ladder Ising models, showing that spontaneous MPT can occur at finite temperature, challenging traditional limitations of 1D systems.

Contribution

The study reveals the existence of spontaneous MPT at finite temperature in 1D ladder Ising models, providing a new paradigm for phase transitions in low-dimensional systems.

Findings

Existence of spontaneous MPT at fixed finite temperature in 1D models

Crossover width exponentially reduced by interactions and decorations

Potential realization of genuine first-order phase transitions in 1D systems

Abstract

The Ising model describes collective behaviors such as phase transitions and critical phenomena in various physical, biological, economical, and social systems. It is well-known that spontaneous phase transition at finite temperature does not exist in the Ising model with short-range interactions in one dimension. Yet, little is known about whether this forbidden phase transition can be approached arbitrarily closely -- at fixed finite temperature. To describe such asymptoticity, here I introduce the notion of marginal phase transition (MPT) and use symmetry analysis of the transfer matrix to reveal the existence of spontaneous MPT at fixed finite temperature $T_0$ in one class of one-dimensional Ising models on decorated two-leg ladders, in which $T_0$ is determined solely by on-rung interactions and decorations, while the crossover width $2\delta T$ is independently, exponentially reduced ($\delta T = 0$ means a genuine phase transition) by on-leg interactions and decorations. These findings establish a simple ideal paradigm for realizing an infinite number of one-dimensional Ising systems with spontaneous MPT, which would be characterized in routine lab measurements as a genuine first-order phase transition with large latent heat thanks to the ultra-narrow $\delta T$ (say less than one nano-kelvin), paving a way to push the limit in our understanding of phase transitions and the dynamical actions of frustration arbitrarily close to the forbidden regime.