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

Non-universal critical behaviour of a mixed-spin Ising model

Non-universal critical behaviour of a mixed-spin Ising model s i S n s j s l s k J J Figure 1. Diagrammatic representation of the extended Kagom´e lattice composed of the mixed spin-1/2 (empty circles) and spin-3/2 (filled circles) sites, respectively. The solid (broken) lines depict the nearest-neighbour (next-nearest-neighbour) interactions.

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

The emergence of integrated information, complexity, and

The Critical, Generalized Ising Model 42 The generalized Ising model acts as this bridge by virtue of the model s ability to 43 exhibit phase transitions and critical points as well as being the simplest (max entropy) 44 model associated with empirical pairwise correlation data [18,24]. Historically, it was 45

Phase transition of a one-dimensional Ising model with

The critical behavior of Ising model on a one-dimensional network, which has long-range connections at distances l > 1 with the probability −m, is studied by using Monte Carlo simulations. Through studying the Ising model on networks with different m values, this paper discusses the impact of the global correlation, which decays with the

Complex-temperature singularities in thed D 2 Ising model

) Ising model on the triangular and honeycomb lattices. There are several reasons for studying the properties of statistical mechanical models with the temperature variable generalized to take on complex values. First, one can understand more deeply the behaviour of various thermodynamic quantities by seeing how they behave as analytic

Critical behaviour of the randomly stirred effects of

behaviour or, under some conditions, to a more complex behaviour described by new non-equilibrium universality classes [13] [22]. In this paper we apply the field theoretic RG to study the effects of turbulent mixing on the critical behaviour of the (generalized) Potts model. Special attention will be paid

Phase Diagram of the Dilute Ising Spin Glass in General

In the Ising case, the nature of the critical point changes for p, p (1since there is a new random fixed point' for finite disorder. Both the Is-ing and Heisenberg models exhibit percolation critical ex-ponents ' near the zero-temperature critical point at p, The Harris criterion' differentiates between cases such as the Ising model, where

Phase transitions and critical behaviour in one-dimensional

of a multitude of 1D Ising critical points, which ends at the PC point. We are interested in the behaviour of the spin system at this end-point. The result is the following. The critical kink-dynamics has a strong influence on the spin-kinetics and even on its statics. Domain growth is governed by criticality: x D 1=Z,

List of Publications

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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The Gonihedric Ising model and (probably not) its dual(s) Author Roll of Honour: G. Savvidy (and sons) F. Wegner T. Jonsson B. Durhuus D. Espriu A. Prats R.K.P.C. Malmini A. Lipowski M. Suzuki E. Cirillo G. Gonnella C. Castelnovo D. Sherrington

Effect of random defects on the critical behaviour of Ising

Effect of random defects on the critical behaviour of Ising models To cite this article: A B Harris 1974 J. Phys. C: Solid State Phys. 7 1671 View the article online for updates and enhancements. Related content Upper bounds for the transition temperatures of generalized Ising models A B Harris-Rigorous upper and lower bounds on the

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].


the side-length, thereby con rming the critical slowdown behavior of the Ising model on Z2. Theorem 1. Consider the critical Ising model on a nite box ˆZ2 of side-length n, i.e. at inverse-temperature c= 1 2 log(1+ p 2). Let gap˝ be the spectral-gap in the generator of the corresponding continuous-time Glauber

E. Burzo Faculty of Physics, Babes-Bolyai University Cluj

Heisenberg model n=3 X-Y model n=2 Ising model n=1 Phase transitions: n→∞ spherical model (Stanley, 1968) n=-2 Gaussian model n can be generalized as continous For d ≥ 4, for all n values, critical behaviour can be described by a model of molecular field approximation

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Dec 09, 2018 near the critical point of the transverse- eld Ising model. II. THE QUANTUM ISING MODEL IN 1D In analogy with its classical counterpart, we study a linear chain of two-state systems, such as spin-1 2 particles, with a speci ed external eld and local couplings. One such model is the transverse- eld Ising model which can be described with the

NPTEL Syllabus - Nonequilibrium Statistical Mechanics

Ising model with nearest-neighbour interaction Mean field theory (MFT) for the Ising model Critical temperature in MFT Critical exponents in MFT 32 Lecture 32: Critical phenomena (Part 4) Definition of specific heat, order parameter, susceptibility and critical isotherm exponents Difference between actual and MFT values of critical exponents

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structural connectome (the generalized Ising model) exhibited similar patterns of the global properties. To study the behavior of the generalized Ising model around criticality, calculation of the dimensionality and critical exponents was performed for the first time, by introducing a new concept of distance based on structural connectivity.

Equilibrium statistical mechanics of lattice models

3.5 Ising Models 36 3.5.1 TheSpin-^ Ising Model 36 3.5.2 TheSpin-1 Ising Model 44 3.6 State-DifferenceModels 45 3.6.1 TheClassical XYModel 45 3.6.2 TheAshkin-Teller Model 53 3.6.3 Potts Models 54 3.6.4 TheStandard Potts Model 55 3.7 Chirality 57 3.7.1 Chiral Potts Models 58 3.7.2 AnExtended 3-State Potts Model on the TriangularLattice 59 3.8

Monte Carlo Study of the Ising Model

variations with homogeneous external fields projected onto the lattice, 1D Ising chain, and examination of the critical temperature of the Ising Model phase transition. The study has let us gain a better understanding of ferromagnetic behaviour in lattices. Background The generalized Ising Model Hamiltonian is written above in Fig. 1. S i, S j

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the two planes. This model can be described in the continuum limit by the following action: A = A1 Is + A 2 Is + m d2x(ε 1(x)+ ε 2(x))+ g d2xσ 1(x)σ 2(x) (2) where Ai Is denotes the action of the critical Ising model, εi(x)the Ising energy operator, σi the Ising spin operator, m∝ (T −T c)and g∝ J.

Phase transitions of geometrically frustrated mixed spin-1/2

it also permits a rather comprehensive analysis of its critical behaviour as well as some basic thermodynamic quantities. Indeed, it directly follows from equation (2.2) that the investigated mixed-spin Ising-Heisenberg model becomes critical if and only if the spin-1/2 Ising model with

Statistical Field Theory - DAMTP

can be generalized to quantum systems. Many systems are formulated on a lattice, such as the Ising model, but as we shall see others which have similar behaviour are continuous systems such as H 20. However, it is useful to have one such model in mind to exemplify the concepts, and we shall use the Ising model in Ddimensions

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Nov 27, 2006 Different Universality Classes have different critical behavior e.g. Ising model, ferromagnet, liquid-gas are in same class XYZ model, with a 3-component spin, is in different class Phase diagram near the critical point Approximate form of thermodynamic functions near the critical point Approximate values of critical Indices

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given sample of a random field Ising model may have Critical behaviour of the random field Ising model is a generalized Vogel-Fulcher law. The ordinary Vogel-Fulcher law [14-21]


Percolation and Critical Behaviour in Many Final Technical dody Systems NOV 76 -NOV 79 6. PERFORMING ORG. REPORT NUMBER 17. AUTHOR q) S. CONTRACT OR GRANU'MBER(e) C. Domb DAER-77-G-007 9. PERFORMING ORGANIZATION NAME AND ADDRES% 10. PROGRAM ELEMENT. PROJECT, TASK AREA & WORK UNIT NUMBERS Kings College Strand, WC2R 2LS, London UK NOV 79

Generalized Gross-Neveu universality class with non-abelian

Large N expansion of generalized non-abelian GN model Large N critical point method of Vasil ev et al determines the critical exponents of the universality class as a function of d = 2 Key ingredient is the universal interaction which is common in all the theories of the universality class whose critical dimension is 2n where n is an integer

The Phase Diagram of the Gonihedric 3d Ising Model via CVM

1 The Model In this paper we discuss the use of the cluster variation method (CVM) in mapping out the phase diagram of the gonihedric 3d Ising model. The gonihedric 3d Ising model is a generalization of the usual 3d Ising model where planar Peierls boundaries between + and −spins can be created at zero energy cost. It has been introduced in

Modeling an auditory stimulated brain under altered states of

line. By simulating the Ising model at different temperatures, Fraiman et al. showed that, at the critical temperature Tc (the temperature at which the system exhibits a transition from an ordered phase to a disor- dered phase), the model can simulate the global behavior of the brain s functional connectivity at rest (Fraiman et al., 2009).

Perturbation theory, scaling and the spherical model

Perturbation theory, scaling and the spherical model 935 an example (Abe 1970).The third kind involves those systems which obey the smoothness postulate. The Ising antiferromagnet is one example, while another is the Ising model

Handout 12. Ising Model - Stanford University

tuation. Hence the 2D Ising model has a critical temperature T c, below which there is spontaneous magnetization and above which there isn t. In other words, there is a phase transition at T c. Unfortunately this doesn t occur in the 1D Ising model. The 1D Ising model does not have a phase transition.

The critical exponents of Ising model systems with pure three

May 22, 2020 Generalized codes and their application to Ising models with four-spin interactions including the eight-vertex model D S Gaunt-Recent citations Monte Carlo study of the pure and dilute Baxter Wu model Nir Schreiber and Joan Adler-Ising model with two-, three- and four-spin interactions K G Chakraborty-Ising model with two-spin interactions and

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Heisenberg model n=3 X-Y model n=2 Ising model n=1 Phase transitions: n spherical model (Stanley, 1968) n=-2 Gaussian model n can be generalized as continous For d 4, for all n values, critical behaviour can be described by a model of molecular field approximation

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Unusual criticality in a generalized 2D XY model Villain Model Unusual critical behavior Ising transition persists untill after it has met the 1/2KT transition Domain walls connecting half vortices e ectively increasing the logrithmic interaction so they dissociate later This is supported by Renormalization Group study!

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understanding, our objective is to develop the generalized Ising model, following the lesson from the two-dimensional Ising model, as the generalized Ising model could be simulated using the anatomical structure of the brain. This model can then be used to study functional information integration and segregation in the brain at rest.

Quantum Phase Transitions in an Integrable One-Dimensional

the critical point of the original model, thus explaining its behaviour. The one-dimensional quantum compass model is shown to be a special case of this generalized model, and is described by a spin liquid with a quantum Ising type of behaviour. The entanglement present in the gen-eralized model is also calculated, showing the absence of