اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدUniversality class of the depinning transition in the two-dimensional Ising model with quenched disorder
167
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
With Monte Carlo methods, we investigate the universality class of the depinning transition in the two-dimensional Ising model with quenched random fields. Based on the short-time dynamic approach, we accurately determine the depinning transition field and both static and dynamic critical exponents. The critical exponents vary significantly with the form and strength of the random fields, but exhibit independence on the updating schemes of the Monte Carlo algorithm. From the roughness exponents $zeta, zeta_{loc}$ and $zeta_s$, one may judge that the depinning transition of the random-field Ising model belongs to the new dynamic universality class with $zeta eq zeta_{loc} eq zeta_s$ and $zeta_{loc} eq 1$. The crossover from the second-order phase transition to the first-order one is observed for the uniform distribution of the random fields, but it is not present for the Gaussian distribution.
قيم البحث
اقرأ أيضاً
Using high-precision Monte-Carlo simulations based on a parallel version of the Wang-Landau algorithm and finite-size scaling techniques we study the effect of quenched disorder in the crystal-field coupling of the Blume-Capel model on the square lat
tice. We mainly focus on the part of the phase diagram where the pure model undergoes a continuous transition, known to fall into the universality class of the pure Ising ferromagnet. A dedicated scaling analysis reveals concrete evidence in favor of the strong universality hypothesis with the presence of additional logarithmic corrections in the scaling of the specific heat. Our results are in agreement with an early real-space renormalization-group study of the model as well as a very recent numerical work where quenched randomness was introduced in the energy exchange coupling. Finally, by properly fine tuning the control parameters of the randomness distribution we also qualitatively investigate the part of the phase diagram where the pure model undergoes a first-order phase transition. For this region, preliminary evidence indicate a smoothening of the transition to second-order with the presence of strong scaling corrections.
With Monte Carlo simulations, we systematically investigate the depinning phase transition in the two-dimensional driven random-field clock model. Based on the short-time dynamic approach, we determine the transition field and critical exponents. The
results show that the critical exponents vary with the form of the random-field distribution and the strength of the random fields, and the roughening dynamics of the domain interface belongs to the new subclass with $zeta eq zeta_{loc} eq zeta_s$ and $zeta_{loc} eq 1$. More importantly, we find that the transition field and critical exponents change with the initial orientations of the magnetization of the two ordered domains.
We present several methods, which utilize symplectic integration techniques based on two and three part operator splitting, for numerically solving the equations of motion of the disordered, discrete nonlinear Schrodinger (DDNLS) equation, and compar
e their efficiency. Our results suggest that the most suitable methods for the very long time integration of this one-dimensional Hamiltonian lattice model with many degrees of freedom (of the order of a few hundreds) are the ones based on three part splits of the systems Hamiltonian. Two part split techniques can be preferred for relatively small lattices having up to $Napprox;$70 sites. An advantage of the latter methods is the better conservation of the systems second integral, i.e. the wave packets norm.
We consider the Ising model on the square lattice with biaxially correlated random ferromagnetic couplings, the critical point of which is fixed by self-duality. The disorder represents a relevant perturbation according to the extended Harris criteri
on. Critical properties of the system are studied by large scale Monte Carlo simulations. The correlation length critical exponent, u=2.005(5), corresponds to that expected in a system with isotropic correlated long-range disorder, whereas the scaling dimension of the magnetization density, x_m=0.1294(7), is somewhat larger than in the pure system. Conformal properties of the magnetization and energy density profiles are also examined numerically.
We use large-scale Monte Carlo simulations to test the Weinrib-Halperin criterion that predicts new universality classes in the presence of sufficiently slowly decaying power-law-correlated quenched disorder. While new universality classes are reason
ably well established, the predicted exponents are controversial. We propose a method of growing such correlated disorder using the three-dimensional Ising model as benchmark systems both for generating disorder and studying the resulting phase transition. Critical equilibrium configurations of a disorder-free system are used to define the two-value distributed random bonds with a small power-law exponent given by the pure Ising exponent. Finite-size scaling analysis shows a new universality class with a single phase transition, but the critical exponents $ u_d=1.13(5), eta_d=0.48(3)$ differ significantly from theoretical predictions. We find that depending on details of the disorder generation, disorder-averaged quantities can develop peaks at two temperatures for finite sizes. Finally, a layer model with the two values of bonds spatially separated to halves of the system genuinely has multiple phase transitions and thermodynamic properties can be flexibly tuned by adjusting the model parameters.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
