Frustration-driven marginal phase transition at finite temperature in an Ising model in one dimension

The Ising model, with simple short-range interactions between constituents (e.g., spins), is a basic mathematical model in statistical mechanics for describing phase transitions in various many-body systems. It was rigorously proven that in one dimension, phase transitions do not exist in this model at any nonzero temperature because the free energy is analytic. Here I show that a family of strongly frustrated one-dimensional Ising model can exhibit a first-order-like phase transition at finite temperature via a virtual level crossing in the free energy, resulting in a large latent heat and an ultranarrow peak in the specific heat [1]. The critical temperature goes to zero as the transition width goes to zero; therefore, this ultranarrow phase transition does not violate the existing theorems and is an extension of the zero-temperature phase transition to the finite temperature regime, thus named marginal phase transition. These exact results expose a mathematical structure and unconventional order parameters that have not appeared before in phase transition problems, shedding new light not only on our understanding of phase transitions and the dynamic actions of frustration but also on one-dimensional device applications. [1] W. Yin, arXiv:2006.08921; arXiv:2006.15087 (2020).