Classical phase transitions in a one-dimensional short-range spin model induced by entropy depletion or complex fields

Abstract

Ising's solution of a classical spin model famously demonstrated the absence of a positive-temperature phase transition in one-dimensional equilibrium systems with short-range interactions. No-go arguments established that the energy cost to insert domain walls in such systems is outweighed by entropy excess so that symmetry cannot be spontaneously broken. An archetypal way around the no-go theorems is to augment interaction energy by increasing the range of interaction. Here we introduce new ways around the no-go theorems by investigating entropy depletion instead. We implement this for the Potts model with invisible states.Because spins in such a state do not interact with their surroundings, they contribute to the entropy but not the interaction energy of the system. Reducing the number of invisible states to a negative value decreases the entropy by an amount sufficient to induce a positive-temperature classical phase transition. This approach is complementary to the long-range interaction mechanism. Alternatively, subjecting positive numbers of invisible states to imaginary or complex fields can trigger such a phase transition. We also discuss potential physical realisability of such systems.

arXiv comment29 pages, 11 figures

References in corpus (36)

• Ising-Type Magnetic Ordering in Atomically Thin FePS3
• Phase Transitions in one-dimensional nonequilibrium systems
• Observation of Lee-Yang zeros
• An omniscient Maxwell's demon
• Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism
• Chromatic roots are dense in the whole complex plane
• General non-existence theorem for phase transitions in one-dimensional systems with short range interactions, and physical examples of such transitions
• Probing Lee-Yang zeros and coherence sudden death
• Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models I. General Theory and Square-Lattice Chromatic Polynomial
• Quadrupolar correlations and spin freezing in S = 1 triangular lattice antiferromagnets
• Novel spin-liquid states in the frustrated Heisenberg antiferromagnet on the honeycomb lattice
• Spanning forests and the q-state Potts model in the limit q \to 0
• Phase Transition Strength through Densities of General Distributions of Zeroes
• Microscopic formulation of the Zimm-Bragg model for the helix-coil transition
• Magnetization plateaus of an exactly solvable spin-1 Ising-Heisenberg diamond chain
• First-Order Transition to Incommensurate Phase with Broken Lattice Rotation Symmetry in Frustrated Heisenberg Model
• Transfer matrix computation of critical polynomials for two-dimensional Potts models
• Phase Transition in Potts Model with Invisible States
• Density of states, Potts zeros, and Fisher zeros of the Q-state Potts model for continuous Q
• Competition for hydrogen bond formation in the helix-coil transition and protein folding
• Exact solution of a classical short-range spin model with a phase transition in one dimension: the Potts model with invisible states
• The three-dimensional, three state Potts model in a negative external field
• Exact results for the zeros of the partition function of the Potts model on finite lattices
• Professor C. N. Yang and Statistical Mechanics
• Phase transitions in one dimension: are they all driven by domain walls?
• Transfer Matrices for the Partition Function of the Potts Model on Toroidal Lattice Strips
• Exact renormalization-group analysis of first order phase transitions in clock models
• Potts Models with Invisible States on General Bethe Lattices
• Dynamical properties of Potts model with invisible states
• Marginal dimensions of the Potts model with invisible states
• Infinite cascades of phase transitions in the classical Ising chain
• Structure of the Partition Function and Transfer Matrices for the Potts Model in a Magnetic Field on Lattice Strips
• Potts Models with (17) Invisible States on Thin Graphs
• Complex-q zeros of the partition function of the Potts model with long-range interactions
• Complex-Temperature Phase Diagrams of 1D Spin Models with Next-Nearest-Neighbor Couplings
• Rigorous Analysis of Renormalization Group Pathologies in the 4-State Clock Model

Cited by in corpus (6)

• Triangle-Well and Ramp Interactions in One-Dimensional Fluids: A Fully Analytic Exact Solution
• Potts Model with Invisible States: A Review
• Solving the one-dimensional Ising chain via mathematical induction: An intuitive approach to the transfer matrix
• Coherence of an extended central spin model with a coupled spin bath
• Ising model with invisible states on scale-free networks
• Ising's roots and the transfer-matrix eigenvalues