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

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.

Revised in response to the referee reports. 28 pages in the preprint format, 6 figures

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• Exact solution of the frustrated Potts model with next-nearest-neighbor interactions in one dimension via AI bootstrapping
• Bifurcation in correlation length of the Ising model on a "Toblerone" lattice
• Quantum Otto engine mimicking Carnot near pseudotransitions in the one-dimensional extended Hubbard model in the atomic limit
• Thermodynamic constraints and pseudotransition behavior in a one-dimensional water-like system
• Spectral mechanism and nearly reducible transfer matrices for pseudotransitions in one-dimensional systems
• Half-ice, half-fire-driven ultranarrow phase crossover in one-dimensional decorated $q$-state Potts ferrimagnets: An AI-co-led exploration