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Register a new userCritical aspects of three-dimensional anisotropic spin-glass models
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We study the $pm J$ three-dimensional Ising model with a longitudinal anisotropic bond randomness on the simple cubic lattice. The random exchange interaction is applied only in the $z$ direction, whereas in the other two directions, $xy$ - planes, we consider ferromagnetic exchange. By implementing an effective parallel tempering scheme, we outline the phase diagram of the model and compare it to the corresponding isotropic one, as well as to a previously studied anisotropic (transverse) case. We present a detailed finite-size scaling analysis of the ferromagnetic - paramagnetic and spin glass - paramagnetic transition lines, and we also discuss the ferromagnetic - spin glass transition regime. We conclude that the present model shares the same universality classes with the isotropic model, but at the symmetric point has a considerably higher transition temperature from the spin-glass state to the paramagnetic phase. Our data for the ferromagnetic - spin glass transition line are supporting a forward behavior in contrast to the reentrant behavior of the isotropic model.
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We report a high-precision finite-size scaling study of the critical behavior of the three-dimensional Ising Edwards-Anderson model (the Ising spin glass). We have thermalized lattices up to L=40 using the Janus dedicated computer. Our analysis takes into account leading-order corrections to scaling. We obtain Tc = 1.1019(29) for the critical temperature, u = 2.562(42) for the thermal exponent, eta = -0.3900(36) for the anomalous dimension and omega = 1.12(10) for the exponent of the leading corrections to scaling. Standard (hyper)scaling relations yield alpha = -5.69(13), beta = 0.782(10) and gamma = 6.13(11). We also compute several universal quantities at Tc.
The three-dimensional bimodal random-field Ising model is investigated using the N-fold version of the Wang-Landau algorithm. The essential energy subspaces are determined by the recently developed critical minimum energy subspace technique, and two implementations of this scheme are utilized. The random fields are obtained from a bimodal discrete $(pmDelta)$ distribution, and we study the model for various values of the disorder strength $Delta$, $Delta=0.5, 1, 1.5$ and 2, on cubic lattices with linear sizes $L=4-24$. We extract information for the probability distributions of the specific heat peaks over samples of random fields. This permits us to obtain the phase diagram and present the finite-size behavior of the specific heat. The question of saturation of the specific heat is re-examined and it is shown that the open problem of universality for the random-field Ising model is strongly influenced by the lack of self-averaging of the model. This property appears to be substantially depended on the disorder strength.
The goal of this work is to show that a ferromagnetic-like domain growth process takes place within the backbone of the three-dimensional $pm J$ Edwards-Anderson (EA) spin glass model. To sustain this affirmation we study the heterogeneities displayed in the out-of-equilibrium dynamics of the model. We show that both correlation function and mean flipping time distribution present features that have a direct relation with spatial heterogeneities, and that they can be characterized by the backbone structure. In order to gain intuition we analyze the pure ferromagnetic Ising model, where we show the presence of dynamical heterogeneities in the mean flipping time distribution that are directly associated to ferromagnetic growing domains. We extend a method devised to detect domain walls in the Ising model to carry out a similar analysis in the three-dimensional EA spin glass model. This allows us to show that there exists a domain growth process within the backbone of this model.
The spatially uniaxially anisotropic d=3 Ising spin glass is solved exactly on a hierarchical lattice. Five different ordered phases, namely ferromagnetic, columnar, layered, antiferromagnetic, and spin-glass phases, are found in the global phase diagram. The spin-glass phase is more extensive when randomness is introduced within the planes than when it is introduced in lines along one direction. Phase diagram cross-sections, with no Nishimori symmetry, with Nishimori symmetry lines, or entirely imbedded into Nishimori symmetry, are studied. The boundary between the ferromagnetic and spin-glass phases can be either reentrant or forward, that is either receding from or penetrating into the spin-glass phase, as temperature is lowered. However, this boundary is always reentrant when the multicritical point terminating it is on the Nishimori symmetry line.
We study the $pm J$ three-dimensional Ising model with a spatially uniaxially anisotropic bond randomness on the simple cubic lattice. The $pm J$ random exchange is applied in the $xy$ planes, whereas in the z direction only a ferromagnetic exchange is used. After sketching the phase diagram and comparing it with the corresponding isotropic case, the system is studied, at the ferromagnetic-paramagnetic transition line, using parallel tempering and a convenient concentration of antiferromagnetic bonds ($p_z=0 ; p_{xy}=0.176$). The numerical data point out clearly to a second-order ferromagnetic-paramagnetic phase transition belonging in the same universality class with the 3d random Ising model. The smooth finite-size behavior of the effective exponents describing the peaks of the logarithmic derivatives of the order parameter provides an accurate estimate of the critical exponent $1/ u=1.463(3)$ and a collapse analysis of magnetization data gives an estimate $beta/ u=0.516(7)$. These results, are in agreement with previous studies and in particular with those of the isotropic $pm J$ three-dimensional Ising at the ferromagnetic-paramagnetic transition line, indicating the irrelevance of the introduced anisotropy.
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