Geometric frustration effects in the spin-1 antiferromagnetic Ising model on the kagome-like recursive lattice: exact results

Jurčišinová, E.; Jurčišin, M.

doi:10.1088/1742-5468/2016/09/093207

Cited by 7 publications

(3 citation statements)

References 26 publications

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“…In doing so, we have found by checking obtained equations numerically that for the case under study with t = 2 the physically plausible expressions for the roots, that have to be real and positive, arise only when the auxiliary partition functions defined for different sub-lattices are equal to each other. Recall that an analogous observation was made for the antiferromagnetic spin-1 model defined on the Husimi lattice [51]. We therefore conclude that on the Husimi lattice with t = 2 there is no alternating order phase.…”

Section: The Husimi Latticesupporting

confidence: 79%

“…Analyses of different physical models on such pseudo-lattices are quite ubiquitous and appear in various physical contexts. We just mention recent studies of antiferromagnetic classical [51,52] and quantum spin models [53], and also several multi-site interaction models [54]. We finally remark that although such approaches usually quite accurately predict the location of the demarkation curves between ordered and disordered phase, as well as the order of the phase transition, they naturally fail to provide correct values of the critical exponents.…”

Section: Modelmentioning

confidence: 95%

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Binary lattice-gases of particles with soft exclusion: exact phase diagrams for tree-like lattices

Shapoval¹,

Dudka²,

Bénichou³

et al. 2021

J. Phys. A: Math. Theor.

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We study equilibrium properties of binary lattice-gases comprising A and B particles, which undergo continuous exchanges with their respective reservoirs, maintained at chemical potentials μ A = μ B = μ. The particles interact via on-site hard-core exclusion and also between the nearest-neighbours: there are a soft repulsion between AB pairs and also interactions of arbitrary strength J, positive or negative, for AA and BB pairs. For tree-like Bethe and Husimi lattices we determine the full phase diagram of such a ternary mixture of particles and voids. We show that for J being above a lattice-dependent threshold value, the critical behaviour is similar: the system undergoes a transition at μ = μ c from a phase with equal mean densities of species into a phase with a spontaneously broken symmetry, in which the mean densities are no longer equal. Depending on the value of J, this transition can be either continuous or of the first order. For sufficiently large negative J, the behaviour on the two lattices becomes markedly different: on the Bethe lattice there exist two separate phases with different kinds of structural order, which are absent on the Husimi lattice, due to stronger frustration effects.

show abstract

Section: The Husimi Latticesupporting

confidence: 79%

Section: Modelmentioning

confidence: 95%

Binary lattice-gases of particles with soft exclusion: exact phase diagrams for tree-like lattices

Shapoval¹,

Dudka²,

Bénichou³

et al. 2021

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…real and positive values) for the roots arise only when the auxiliary partition functions defined for different sublattices are equal to each other. Recall that an analogous observation was made for the antiferromagnetic spin-1 model defined on the Husimi lattice [51]. We therefore conclude that for t = 2, i.e.…”

Section: Introducing Next Auxiliary Variablessupporting

confidence: 79%

Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices

Shapoval,

Dudka,

Bénichou

et al. 2021

Preprint

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We study equilibrium properties of binary lattice-gases comprising A and B particles, which undergo continuous exchanges with their respective reservoirs, maintained at chemical potentials µ A = µ B = µ. The particles interact via onsite hard-core exclusion and also between the nearest-neighbours: there are a soft repulsion for AB pairs and interactions of arbitrary strength J, positive or negative, for AA and BB pairs. For tree-like Bethe and Husimi lattices we determine the full phase diagram of such a ternary mixture of particles and voids. We show that for J being above a lattice-dependent threshold value, the critical behaviour is similar: the system undergoes a transition at µ = µ c from a phase with equal mean densities of species into a phase with a spontaneously broken symmetry, in which the mean densities are no longer equal. Depending on the value of J, this transition can be either continuous or of the first order. For sufficiently big negative J, the behaviour on the two lattices becomes markedly different: while for the Bethe lattice there exists a continuous transition into a phase with an alternating order followed by a continuous re-entrant transition into a disordered phase, an alternating order phase is absent on the Husimi lattice due to strong frustration effects.

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Isothermal Entropy Change for the Spin-1 Blume-Capel Model on the Bethe Lattice

Albayrak

2019

Int J Theor Phys

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Geometric frustration effects in the spin-1 antiferromagnetic Ising model on the kagome-like recursive lattice: exact results

Cited by 7 publications

References 26 publications

Binary lattice-gases of particles with soft exclusion: exact phase diagrams for tree-like lattices

Binary lattice-gases of particles with soft exclusion: exact phase diagrams for tree-like lattices

Binary lattice-gases of particles with soft exclusion: Exact phase diagrams for tree-like lattices

Isothermal Entropy Change for the Spin-1 Blume-Capel Model on the Bethe Lattice

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