Equation of state from the Potts-percolation model of a solid

Kaufman, Miron; Diep, H. T.

doi:10.1103/physreve.84.051106

Phys. Rev. E

2011

DOI: 10.1103/physreve.84.051106

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Equation of state from the Potts-percolation model of a solid

Miron Kaufman

H. T. Diep

Abstract: We expand the Potts-percolation model of a solid to include stress and strain.Neighboring atoms are connected by bonds. We set the energy of a bond to be given by the Lennard-Jones potential. If the energy is larger than a threshold the bond is more likely to fail, while if the energy is lower than the threshold the bond is more likely to be alive. In two dimensions we compute the equation of state: stress as function of inter-atomic distance and temperature by using renormalization group and Monte Carlo simul… Show more

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Cited by 4 publications

References 19 publications

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Oddq-state clock spin-glass models in three dimensions, asymmetric phase diagrams, and multiple algebraically ordered phases

İlker

Berker

2014

Phys. Rev. E

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Distinctive orderings and phase diagram structures are found, from renormalization-group theory, for odd q-state clock spin-glass models in d = 3 dimensions. These models exhibit asymmetric phase diagrams, as is also the case for quantum Heisenberg spin-glass models. No finite-temperature spin-glass phase occurs. For all odd q 5, algebraically ordered antiferromagnetic phases occur. One such phase is dominant and occurs for all q 5. Other such phases occupy small low-temperature portions of the phase diagrams and occur for 5 q 15. All algebraically ordered phases have the same structure, determined by an attractive finite-temperature sink fixed point where a dominant and a subdominant pair states have the only nonzero Boltzmann weights. The phase transition critical exponents quickly saturate to the high q value.

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Oddq-state clock spin-glass models in three dimensions, asymmetric phase diagrams, and multiple algebraically ordered phases

İlker

Berker

2014

Phys. Rev. E

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Lower-critical spin-glass dimension from 23 sequenced hierarchical models

2015

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The lower-critical dimension for the existence of the Ising spin-glass phase is calculated, numerically exactly, as d L = 2.520 for a family of hierarchical lattices, from an essentially exact (correlation coefficent R 2 = 0.999 999) near-linear fit to 23 different diminishing fractional dimensions. To obtain this result, the phase transition temperature between the disordered and spin-glass phases, the corresponding critical exponent y T , and the runaway exponent y R of the spin-glass phase are calculated for consecutive hierarchical lattices as dimension is lowered.

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Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of thes=3/2Ising model from renormalization-group theory

et al. 2016

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The spin-3 2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d = 3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d = 3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.

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Equation of state from the Potts-percolation model of a solid

Cited by 4 publications

References 19 publications

Oddq-state clock spin-glass models in three dimensions, asymmetric phase diagrams, and multiple algebraically ordered phases

Oddq-state clock spin-glass models in three dimensions, asymmetric phase diagrams, and multiple algebraically ordered phases

Lower-critical spin-glass dimension from 23 sequenced hierarchical models

Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of thes=3/2Ising model from renormalization-group theory

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