# Critical Behaviour Of A Generalized Ising Model

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### Abstract arXiv:1802.00181v1 [cond-mat.stat-mech] 1 Feb 2018

The ground state, zero-temperature magnetization process, critical behaviour and isothermal entropy change of the mixed-spin Ising model on a decorated triangular lattice in a magnetic ﬁeld are exactly studied after performing the generalized decoration-iteration mapping transformation.

### The Emergence of Integrated Information, Complexity, and

to classical Ising motifs with N = 200 nodes while modelling the brain [12]. This paper aims to demonstrate the critical properties of F extend to different network connectivities with dynamics governed by the generalized Ising model. The generalized Ising model has been shown to simulate the statistical behavior of the brain [12 15].

### The Planar Ising Model and Total Positivity

later generalized by Björnberg to the setting of quantum Ising models [5]. Also, a new dis-tributional relation between random currents, Bernoulli percolation and the FK-Ising model wasdiscoveredbyLupuandWerner[27]. One of the main tools used to study the random current model is the switching lemma [15], and our result may be thought of as its

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### PDF/1982/03/jphys 1982 43 3 475 0.pdf

in the study of the Ising model, many authors used this approach to calculate the critical behaviour of other models like generalized Ising models [2], Ising antiferromagnets in a magnetic field [3, 4], lattice gas models [4], quantum spin systems [5], Lee and Yang singularities [6]. For all these models, the transfer

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25. F. Iglói: Conformal invariance and critical behaviour of the quantum Ashkin-Teller chain near the decoupling limit Nucl. Phys. B5A, 15 (1988) 26. F. Iglói and J. Zittartz: The Ising transition lines of the symmetric Ashkin-Teller model Z. Physik B73, 125 (1988) 27. F. Iglói: Quantum Ising model on a quasiperiodic lattice J. Phys. A21

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### Dragi Karevski To cite this version

describing the XX-model which has U(1) symmetry. We will consider here only free boundary conditions. The phase diagram and the critical behaviour of this model are known exactly since the work of Barouch and McCoy in 1971 [28, 29] who generalized results obtained previously in the case of a vanishing transverse ﬁeld [1], or at κ= 1 [27].

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