Frustration-driven unconventional phase transitions at finite temperature in a one-dimensional ladder Ising model

Abstract

The Ising model, with short-range interactions between constituents, is a basic mathematical model in statistical mechanics [1]. It has been widely used to describe collective phenomena such as order-disorder phase transitions in various physical, biological, economical, and social systems. However, it was proven that spontaneous phase transitions do not exist in the one-dimensional Ising models [2]. Besides low dimensionality, frustration is the other well-known suppressor of phase transitions [3].Here I show that surprisingly, a strongly frustrated one-dimensional two-leg ladder Ising model can exhibit a marginal finite-temperature phase transition. It features a large latent heat, a sharp peak in specific heat, and unconventional order parameters, which classify the transition as involving an entropy-favored intermediate-temperature ordered state and further unveil a crossover to an exotic "normal state" in which frustration effectively decouples the two strongly interacted legs in a counterintuitive nonmean-field way. These exact results expose a mathematical structure that has not appeared before in phase-transition problems, and shed new light on our understanding of phase transitions and the dynamical actions of frustration. Applications of this model and its mechanisms to various systems with extensions to consider higher dimensions, quantum characters, or external fields, etc. are anticipated and briefly discussed-with insights into the puzzling phenomena of strange strong frustration [4] and intermediate-temperature orders such as the Bozin-Billinge orbital-degeneracylifting [5] recently discovered in real materials.

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

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Very recently, the discovery of a marginal, or practically perfect, phase transition (MPT or PPPT) at finite temperature in the 2-leg ladder Ising model with trimer rungs was reported [1]. The MPT or PPPT stems from a new mathematical structure that has not appeared before in phase-transition problems.

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Dimerization and spin-decoupling in two-leg Heisenberg ladder with frustrated trimer rungs

“…This arrangement is conducive to several interesting effects. In its classical Ising limit, the system exhibits a frustration-driven ultra-narrow phase crossover at finite temperature [6,7]. For the quantum case, as we will demonstrate here, the excitation spectrum contains a soft gapless mode separated from the other excitations by a gap in the limit of weak interchain coupling J 2 , J 3 J 1 .…”

“…Based on this, one may suspect that the dimerized phase persists even if a NN coupling is explicitly turned on also in between the center spins in the Hamiltonian. The resulting projected model results in the altered orbital Hamiltonian (6).…”

“…2]. Because the 3-leg Hamiltonian in (6) has no linear offset to the orbital magnetic field as discussed with Eq. ( 4), at the same time as turning on J 1 , J 2 is tuned linearly towards J 3 , i.e., α = 0, as indicated with Fig.…”

Emergence of spinons in layered trimer iridate Ba4Ir3O10

“…3 This behavior differs from that expected in 1D systems, where the weak inter-chain coupling leads to multiple bound triplon states in addition to the spinon continuum [9,52,53]. The lack of sharp bound states in the experimental data is therefore inconsistent with the weak coupling model, which leads us to another explanation, a strong coupling model [54,55]. In this model, the intra-trimer AFM interactions J 1 and J 3 are substantial and compete with each other, making the trimer resemble a triangular unit in a triangular lattice [Fig.…”