Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSheared Ising models in three dimensions
173
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
The nonequilibrium phase transition in sheared three-dimensional Ising models is investigated using Monte Carlo simulations in two different geometries corresponding to different shear normals. We demonstrate that in the high shear limit both systems undergo a strongly anisotropic phase transition at exactly known critical temperatures T_c which depend on the direction of the shear normal. Using dimensional analysis, we determine the anisotropy exponent theta=2 as well as the correlation length exponents nu_parallel=1 and nu_perp=1/2. These results are verified by simulations, though considerable corrections to scaling are found. The correlation functions perpendicular to the shear direction can be calculated exactly and show Ornstein-Zernike behavior.
rate research
Read More
We investigate by Monte Carlo simulations the critical properties of the three-dimensional bond-diluted Ising model. The phase diagram is determined by locating the maxima of the magnetic susceptibility and is compared to mean-field and effective-medium approximations. The calculation of the size-dependent effective critical exponents shows the competition between the different fixed points of the model as a function of the bond dilution.
Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a 5-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions as a function of the strength of the interlayer interaction.
We study the critical behavior of the Ising model in three dimensions on a lattice with site disorder by using Monte Carlo simulations. The disorder is either uncorrelated or long-range correlated with correlation function that decays according to a power-law $r^{-a}$. We derive the critical exponent of the correlation length $ u$ and the confluent correction exponent $omega$ in dependence of $a$ by combining different concentrations of defects $0.05 leq p_d leq 0.4$ into one global fit ansatz and applying finite-size scaling techniques. We simulate and study a wide range of different correlation exponents $1.5 leq a leq 3.5$ as well as the uncorrelated case $a = infty$ and are able to provide a global picture not yet known from previous works. Additionally, we perform a dedicated analysis of our long-range correlated disorder ensembles and provide estimates for the critical temperatures of the system in dependence of the correlation exponent $a$ and the concentrations of defects $p_d$. We compare our results to known results from other works and to the conjecture of Weinrib and Halperin: $ u = 2/a$ and discuss the occurring deviations.
We investigate the two-dimensional $q=3$ and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number $z$ of equivalent neighbors. For not too large $z$, the transitions fit well in the universality classes of the short-range Potts models. However, at longer ranges the transitions become discontinuous. For $q=3$ we locate a tricritical point separating the continuous and discontinuous transitions near $z=80$, and a critical fixed point between $z=8$ and 12. For $q=4$ the transition becomes discontinuous for $z > 16$. The scaling behavior of the $q=4$ model with $z=16$ approximates that of the $q=4$ merged critical-tricritical fixed point predicted by the renormalization scenario.
We consider the three-dimensional Ising model slightly below its critical temperature, with boundary conditions leading to the presence of an interface. We show how the interfacial properties can be deduced starting from the particle modes of the underlying field theory. The product of the surface tension and the correlation length yields the particle density along the string whose propagation spans the interface. We also determine the order parameter and energy density profiles across the interface, and show that they are in complete agreement with Monte Carlo simulations that we perform.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
