Efficient search method for obtaining critical properties (original) (raw)
Critical phenomena in 1D Ising model with arbitrary spin
EPJ Web of Conferences
The aim of this work was to study critical phenomena taking place in 1D Ising model with different exchange interactions signs and arbitrary spin values in a magnetic field. Exact analytical formulas for frustration fields, zero temperature magnetization and entropy at these fields are obtained. The general behavior of pair spin correlation function with the accounting of only interactions between nearest neighbors is examined.
Locating analytically critical temperatures in some statistical systems
Physical Review B, 1994
We have found a simple criterion which allows for the straightforward determination of the order-disorder critical temperatures. The method reproduces exactly results known for the two dimensional Ising, Potts and Z(N < 5) models. It also works for the Ising model on the triangular lattice. For systems which are not selfdual our proposition remains an unproven conjecture. It predicts β c = 0.2656... for the two coupled layers of Ising spins. Critical temperature of the three dimensional Ising model is related to the free energy of the two layer Ising system.
Revista Mexicana de Fisica
We used a Monte Carlo simulation to analize the magnetic behavior of Ising model of mixed spins S A i = ±3/2, ±1/2 and σ B j = ±5/2, ±3/2, ±1/2, on a square lattice. Were studied the possible critical phenomena that may emerge in the region around the multiphase point (D/|J1| = −3, J2/|J1| = 1) and the dependence of the phase diagrams with the intensities of the anisotropy field of single ion (D/|J 1 |) and the ferromagnetic coupling of exchange spin S A i (J 2 /|J 1 |). The system displays first order phase transitions in a certain range of the parameters of the Hamiltonian, which depend on D/|J 1 | and |J 2 /|J 1 |. In the plane (D/|J 1 |, k B T /|J 1 |), the decrease of |D/|J 1 ||, implies that the critical temperature, T c , increases and the first order transition temperature, T t , decreases. In the plane (J2/|J1|, kBT /|J1|), Tc increases with the increasing of J2/|J1|, while that Tt decreases.
Critical dynamics of slightly disordered spin systems
Journal of Experimental and Theoretical Physics, 1998
͑Submitted 4 December 1997͒ Zh. É ksp. Teor. Fiz. 114, 972-984 ͑September 1998͒ This paper is a field theoretic description of the critical dynamics of spin systems with frozen nonmagnetic impurities. For three-dimensional systems the dynamical critical exponent is found directly by employing the three-loop approximation with the Padé -Borel summation technique. The results are compared with those obtained by calculating the dynamical exponent for homogeneous systems in the four-loop approximation, and with the values obtained by computer simulation of the critical dynamics by Monte Carlo methods. Calculations of the dynamical exponent for the two-dimensional Ising model in the four-loop approximation are also presented.
Influence of an Initial States on the Critical Relaxation of Ising-like Spin Systems
Journal of Siberian Federal University. Mathematics & Physics, 2018
The non-equilibrium critical behaviour of the three-dimensional pure and site-diluted spin systems described by Ising model is studied for different spin concentrations with evolution from various initial magnetic states. The universal scaling functions are determined for the magnetization.
On the critical dynamics of one-dimensional Ising models
Physics Letters A, 1986
The critical dynamics of an Ising ferromagnetic chain with two different coupling constants (J1>J2) is studied. The dynamical critical exponent z is found to be nonuniversal. For Glauber dynamics one finds z = 1+J1/J2, while for Kawasaki dynamics z = 3+2J1/J2. The case of a disordered chain is also briefly discussed.
Entropy, 2018
The mixed spin-1/2 and spinS Ising model on the Union Jack (centered square) lattice with four different three-spin (triplet) interactions and the uniaxial single-ion anisotropy is exactly solved by establishing a rigorous mapping equivalence with the corresponding zero-field (symmetric) eight-vertex model on a dual square lattice. A rigorous proof of the aforementioned exact mapping equivalence is provided by two independent approaches exploiting either a graph-theoretical or spin representation of the zero-field eight-vertex model. An influence of the interaction anisotropy as well as the uniaxial single-ion anisotropy on phase transitions and critical phenomena is examined in particular. It is shown that the considered model exhibits a strong-universal critical behaviour with constant critical exponents when considering the isotropic model with four equal triplet interactions or the anisotropic model with one triplet interaction differing from the other three. The anisotropic models with two different triplet interactions, which are pairwise equal to each other, contrarily exhibit a weak-universal critical behaviour with critical exponents continuously varying with a relative strength of the triplet interactions as well as the uniaxial single-ion anisotropy. It is evidenced that the variations of critical exponents of the mixed-spin Ising models with the integer-valued spins S differ basically from their counterparts with the half-odd-integer spins S.
Physical Review E, 1999
The equilibrium ensemble approach to disordered systems is used to investigate the critical behaviour of the two dimensional Ising model in presence of quenched random site dilution. The numerical transfer matrix technique in semi-infinite strips of finite width, together with phenomenological renormalization and conformal invariance, is particularly suited to put the equilibrium ensemble approach to work. A new method to extract with great precision the critical temperature of the model is proposed and applied. A more systematic finite-size scaling analysis than in previous numerical studies has been performed. A parallel investigation, along the lines of the two main scenarios currently under discussion, namely the logarithmic corrections scenario (with critical exponents fixed in the Ising universality class) versus the weak universality scenario (critical exponents varying with the degree of disorder), is carried out. In interpreting our data, maximum care is constantly taken to be open in both directions. A critical discussion shows that, still, an unambiguous discrimination between the two scenarios is not possible on the basis of the available finite size data.
Critical behavior of the classical spin-1 Ising model for magnetic systems
AIP Advances, 2022
In this work, the critical properties of the classical spin-1 Ising Hamiltonian applied to magnetic systems characterized by the first-neighbors biquadratic exchange, the anisotropy and the external magnetic field contributions are theoretically investigated. The first-neighbors bilinear exchange interaction is set equal to zero. For magnetic systems the bicubic exchange interaction must be set equal to zero as it would break the time-reversal invariance of the exchange Hamiltonian. To determine the critical behavior, the spin-1 Ising Hamiltonian is mapped onto the spin-1/2 Ising Hamiltonian by using the Griffith’s variable transformation. The critical surface of a 2D square magnetic lattice is determined in the parameter space as a function of the magnetic parameters and the phase transition occurring across it is quantitatively discussed by calculating, for each spin, the free energy and the magnetization. The free energy of the 2D square magnetic lattice, described via the three-...
Journal of the Physical Society of Japan, 2008
Values of dynamic critical exponents are numerically estimated for various models with the nonequilibrium relaxation method to test the dynamic universality hypothesis. The dynamics used here are single-spin update with Metropolis-type transition probabities. The estimated values of nonequilibrium relaxation exponent of magnetization lambdam (=beta/znu) of Ising models on bcc and fcc lattices are estimated to be 0.251(3) and 0.252(3), respectively, which are consistent with the value of the model on simple-cubic lattice, 0.250(2). The dynamic critical exponents of three-states Potts models on square, honeycomb and triangular lattices are also estimated to be 2.193(5), 2.198(4), and 2.199(3), respectively. They are consistent within the error bars. It is also confirmed that Ising models with regularly modulated coupling constants on square lattice have the same dynamic critical exponents with the uniformly ferromagnetic Ising model.