A minimal exactly solved model with the extreme Thouless effect

Abstract

We present and analyze a minimal exactly solved model that exhibits a mixed-order phase transition known in the literature as the Thouless effect. Such hybrid transitions do not fit into the modest classification of thermodynamic transitions and as such, they used to be overlooked or incorrectly identified in the past. The recent series of observations of such transitions in many diverse systems suggest that a new taxonomy of phase transitions is needed. The spin model we present due to its simplicity and possible experimental designs could bring us to this goal. We find the Hamiltonian of the model from which partition function is easily calculated. Thermodynamic properties of the model, i.e. discontinuous magnetization and diverging susceptibility, are discussed. Finally, its generalizations and further research directions are proposed.

4 pages, 2 figures

References in corpus (5)

• Explosive percolation via control of the largest cluster
• Avoiding a Spanning Cluster in Percolation Models
• Mixed order transition and condensation in exactly soluble one dimensional spin model
• Extraordinary variability and sharp transitions in a maximally frustrated dynamic network
• Extreme Thouless effect in a minimal model of dynamic social networks

Cited by in corpus (5)

• Nonequilibrium phases and phase transitions of the XY-model
• Mixed-order phase transition in a minimal, diffusion based spin model
• Partial equivalence of statistical ensembles in a simple spin model with discontinuous phase transitions
• Fluctuations and Correlations in a Model of Extreme Introverts and Extroverts
• Exact results for the extreme Thouless effect in a model of network dynamics