The Hintermann–Merlini–Baxter–Wu and the infinite-coupling-limit Ashkin–Teller models

Huang, Yuan; Deng, Youjin; Jacobsen, Jesper Lykke; Salas, José Valero

doi:10.1016/j.nuclphysb.2012.11.015

Cited by 11 publications

(7 citation statements)

References 67 publications

(162 reference statements)

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“…Given the central role played by tricritical points in Potts model physics 43 , characterization of this new tricriticality (critical exponents as well as determination of its conformal field theory) remains an exciting challenge that we hope to address in the future. One could also imagine studying the role of quantum fluctuations in other statistical models with multi-spin interactions such as the Hintermann-Merlini-Baxter-Wu generalizations on any plane Eulerian triangulation 45 . We also point to a recent reference 46 where the case of a classical magnetic field was considered: a classical Monte-Carlo analysis indicate a different universality class (ν = 1, α = 1/2, β = 3/4), however the critical exponents violate scaling relations so that further work should clarify this.…”

Section: Discussionmentioning

confidence: 99%

Baxter-Wu model in a transverse magnetic field

et al. 2014

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We investigate the low-energy properties as well as quantum and thermal phase transitions of the Baxter-Wu model in a transverse magnetic field. Our study relies on stochastic series expansion quantum Monte Carlo and on series expansions about the low- and high-field limits at zero temperature using the quantum finite-lattice method on the triangular lattice. The phase boundary consists of a second-order critical line in the four-state Potts model universality class starting from the pure Baxter-Wu limit meeting a first-order line connected to the zero-temperature transition point (h≈2.4, T=0). Both lines merge at a tricritical point approximately located at (h≈2.3J, T≈J).

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Section: Discussionmentioning

confidence: 99%

Baxter-Wu model in a transverse magnetic field

et al. 2014

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“…Remark 4.4. The six-vertex model considered in this paper can be obtained as an infinite-coupling limit of the mixed Ashkin-Teller model in the sense of [30]. By a calculation inspired by the one presented in [12], one can obtain the superimposed model as the limit of an FK representation of the mixed Ashkin-Teller model.…”

Section: The Superimposed Model As a Graphical Representation Of The ...mentioning

confidence: 99%

Finitary codings for gradient models and a new graphical representation for the six-vertex model

Ray,

Spinka

2019

Preprint

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It is known that the Ising model on Z d at a given temperature is a finitary factor of an i.i.d. process if and only if the temperature is at least the critical temperature. Below the critical temperature, the plus and minus states of the Ising model are distinct and differ from one another by a global flip of the spins. We show that it is only this global information which poses an obstruction for being finitary by showing that the gradient of the Ising model is a finitary factor of i.i.d. at all temperatures. As a consequence, we deduce a volume-order large deviation estimate for the energy. A similar result is shown for the Potts model.A result in the same spirit is also shown for the six-vertex model, which is itself the gradient of a height function, with parameter c 6.4. We show that the gradient of the height function is not a finitary factor of an i.i.d. process, but that its "Laplacian" is. For this, we introduce a coupling between the six-vertex model with c ≥ 2 and a new graphical representation of it, reminiscent of the Edwards-Sokal coupling between the Potts and random-cluster models. We believe that this graphical representation may be of independent interest and could serve as a tool in further understanding of the six-vertex model.To provide further support for the ubiquity of this type of phenomenon, we also prove an analogous result for the so-called beach model.The tools and techniques used in this paper are probabilistic in nature. The heart of the argument is to devise a suitable tree structure on the clusters of the underlying percolation process (associated to the graphical representation of the given model), which can be revealed piece-by-piece via exploration.

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“…Recent researches of this Ising model and its phase diagrams with four spin interaction and some of its applications have been done [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Numerical study of the spin-3/2 Ashkin-Teller model

Boudefla¹,

Bekhechi²,

Hontinfinde³

2015

Condens. Matter Phys.

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The study of the Ashkin-Teller model (ATM) of spin-3/2 on a hypercubic lattice is undertaken via Monte Carlo simulation. The phase diagrams are displayed and discussed in the physical parameter space. Rich physical properties are recovered, namely the second order transition and multicritical points. The phase diagrams have been obtained by varying the strength describing the four spin interaction and the single ion potential. This model shows a new high temperature partially ordered phase, called 〈S〉 and a new Baxter 3/2 ground state which do not exist either in the spin-1/2 ATM or in the spin-1 ATM.

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The Hintermann–Merlini–Baxter–Wu and the infinite-coupling-limit Ashkin–Teller models

Cited by 11 publications

References 67 publications

Baxter-Wu model in a transverse magnetic field

Baxter-Wu model in a transverse magnetic field

Finitary codings for gradient models and a new graphical representation for the six-vertex model

Numerical study of the spin-3/2 Ashkin-Teller model

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