Mixed order transition and condensation in exactly soluble one dimensional spin model

Abstract

Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far from thermal equilibrium. In a recent paper [1] an exactly soluble spin model with long-range interactions that exhibits MOT was introduced and analyzed both by a grand canonical calculation and a renormalization group analysis. The model was shown to lay a bridge between two classes of one dimensional models exhibiting MOT, namely between spin models with inverse distance square interactions and surface depinning models. In this paper we elaborate on the calculations done in [1]. We also analyze the model in the canonical ensemble, which yields a better insight into the mechanism of MOT. In addition, we generalize the model to include Potts and general Ising spins, and also consider a broader class of interactions which decay with distance with a power law different from 2.

arXiv comment36 pages, 11 figures; Updated affiliation and email of authors

References in corpus (18)

• Theory of Phase Ordering Kinetics
• The large deviation approach to statistical mechanics
• Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
• "Explosive Percolation" Transition is Actually Continuous
• Why is the DNA Denaturation Transition First Order?
• Classical critical behavior of spin models with long-range interactions
• Jamming Percolation and Glass Transitions in Lattice Models
• Core percolation on complex networks
• Discontinuous Percolation Transitions in Epidemic Processes, Surface Depinning in Random Media and Hamiltonian Random Graphs
• Criticality in one dimension with inverse square-law potentials
• Logarithmic Conformal Field Theory: a Lattice Approach
• The Lee-Yang theory of equilibrium and nonequilibrium phase transitions
• Phase diagram of the mean field model of simplicial gravity
• Melting and unzipping of DNA
• Phase transition in a non-conserving driven diffusive system
• Extraordinary variability and sharp transitions in a maximally frustrated dynamic network
• Phase Ordering in One-Dimensional Systems with Long-Range Interactions
• Denaturation of Circular DNA: Supercoil Mechanism

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