scholarly journals Investigation of Finite-Size 2D Ising Model with a Noisy Matrix of Spin-Spin Interactions

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 585 ◽  
Author(s):  
Boris Kryzhanovsky ◽  
Magomed Malsagov ◽  
Iakov Karandashev
Keyword(s):  
Ising Model ◽  
Ground State ◽  
Multiplicative Noise ◽  
Finite Size ◽  
Gradual Change ◽  
Linear Dimensions ◽  
Spin Interactions ◽  
Glass Model ◽  
Analytical Expressions ◽  
Uncorrelated State

We analyze changes in the thermodynamic properties of a spin system when it passes from the classical two-dimensional Ising model to the spin glass model, where spin-spin interactions are random in their values and signs. Formally, the transition reduces to a gradual change in the amplitude of the multiplicative noise (distributed uniformly with a mean equal to one) superimposed over the initial Ising matrix of interacting spins. Considering the noise, we obtain analytical expressions that are valid for lattices of finite sizes. We compare our results with the results of computer simulations performed for square N = L × L lattices with linear dimensions L = 50 ÷ 1000. We find experimentally the dependencies of the critical values (the critical temperature, the internal energy, entropy and the specific heat) as well as the dependencies of the energy of the ground state and its magnetization on the amplitude of the noise. We show that when the variance of the noise reaches one, there is a jump of the ground state from the fully correlated state to an uncorrelated state and its magnetization jumps from 1 to 0. In the same time, a phase transition that is present at a lower level of the noise disappears.

scholarly journals Analytical expressions for a finite-size 2D Ising model

2017 ◽  
Vol 26 (3) ◽  
pp. 165-171 ◽  
Author(s):  
I. M. Karandashev ◽  
B. V. Kryzhanovsky ◽  
M. Yu. Malsagov
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Analytical Expressions

QUANTUM PHASE TRANSITION AND ENTANGLEMENT IN THE TRANSVERSE-FIELD ISING MODEL

2006 ◽  
Vol 04 (04) ◽  
pp. 705-713 ◽  
Author(s):  
JUNPENG CAO ◽  
GANG XIONG ◽  
YUPENG WANG ◽  
X. R. WANG
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Quantum Phase Transition ◽  
Ground State ◽  
Transverse Field ◽  
Quantum Phase ◽  
Global Entanglement ◽  
Transverse Field Ising Model ◽  
Analytical Expressions ◽  
Number Of Particles

We present an exact calculation of the global entanglement for the ground state of the transverse-field Ising model. We obtain the analytical expressions for the correlation functions, concurrence and the global entanglement of the system for arbitrary number of particles in the ground state. We prove that the inflexion of the global entanglement exactly corresponds to the quantum phase transition point of the system.

scholarly journals DYNAMIC CRITICAL EXPONENTS OF THE ISING MODEL WITH MULTISPIN INTERACTIONS

2001 ◽  
Vol 15 (15) ◽  
pp. 487-496 ◽  
Author(s):  
C. S. SIMÕES ◽  
J. R. DRUGOWICH DE FELÍCIO
Keyword(s):  
Ising Model ◽  
Potts Model ◽  
Critical Exponents ◽  
Finite Size ◽  
Two Dimensions ◽  
Time Dynamics ◽  
Spin Interactions ◽  
Dynamic Exponent ◽  
Short Time ◽  
Multispin Interactions

We revisit the short-time dynamics of 2D Ising model with three spin interactions in one direction and estimate the critical exponents z, θ, β and ν. Taking properly into account the symmetry of the Hamiltonian, we obtain results completely different from those obtained by Wang et al.10 For the dynamic exponent z our result coincides with that of the 4-state Potts model in two dimensions. In addition, results for the static exponents ν and β agree with previous estimates obtained from finite size scaling combined with conformal invariance. Finally, for the new dynamic exponent θ we find a negative and close to zero value, a result also expected for the 4-state Potts model according to Okano et al.

THE GROUND-STATE PHASE DIAGRAMS OF THE SPIN-2 ISING MODEL

2007 ◽  
Vol 21 (31) ◽  
pp. 5265-5274 ◽  
Author(s):  
AHMET ERDİNÇ
Keyword(s):  
Magnetic Field ◽  
Ising Model ◽  
External Magnetic Field ◽  
Phase Diagrams ◽  
Crystal Field ◽  
Ground State ◽  
Exchange Interactions ◽  
Nearest Neighbors ◽  
Biquadratic Exchange ◽  
Model Hamiltonian

The ground-state phase diagrams are obtained for the spin-2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. Obtained phase diagrams are presented in the (Δ,J), (K,J), (Δ/J,K/J), (Δ/|J|,K/|J|), (Δ/|K|,J/|K|), (H/J,Δ/J), (H/|J|,Δ/|J|), (H/J,K/J), and (H/|J|,K/|J|) planes where J, K, Δ, and H are the bilinear, biquadratic exchange interactions, the single-ion crystal field, and the external magnetic field, respectively. The influence of the external magnetic field on the spin configurations is investigated.

scholarly journals Finite-size behavior of the critical Ising model on a rectangle with free boundaries

2012 ◽  
Vol 86 (4) ◽  
Author(s):  
Xintian Wu ◽  
Nickolay Izmailian ◽  
Wenan Guo
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Free Boundaries

scholarly journals Anisotropic scaling of the two-dimensional Ising model II: surfaces and boundary fields

2020 ◽  
Vol 8 (3) ◽  
Author(s):  
Hendrik Hobrecht ◽  
Fred Hucht
Keyword(s):  
Ising Model ◽  
Boundary Conditions ◽  
Scaling Limit ◽  
Finite Size ◽  
Square Lattice ◽  
Conformal Field ◽  
Anisotropic Scaling ◽  
Finite Lattices ◽  
Antiferromagnetic Ising Model ◽  
Boundary Fields

Based on the results published recently [SciPost Phys. 7, 026 (2019)], the influence of surfaces and boundary fields are calculated for the ferromagnetic anisotropic square lattice Ising model on finite lattices as well as in the finite-size scaling limit. Starting with the open cylinder, we independently apply boundary fields on both sides which can be either homogeneous or staggered, representing different combinations of boundary conditions. We confirm several predictions from scaling theory, conformal field theory and renormalisation group theory: we explicitly show that anisotropic couplings enter the scaling functions through a generalised aspect ratio, and demonstrate that open and staggered boundary conditions are asymptotically equal in the scaling regime. Furthermore, we examine the emergence of the surface tension due to one antiperiodic boundary in the system in the presence of symmetry breaking boundary fields, again for finite systems as well as in the scaling limit. Finally, we extend our results to the antiferromagnetic Ising model.

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