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Register a new userSpecific-heat exponent and modified hyperscaling in the 4D random-field Ising model
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We report a high-precision numerical estimation of the critical exponent $alpha$ of the specific heat of the random-field Ising model in four dimensions. Our result $alpha = 0.12(1)$ indicates a diverging specific-heat behavior and is consistent with the estimation coming from the modified hyperscaling relation using our estimate of $theta$ via the anomalous dimensions $eta$ and $bar{eta}$. Our analysis benefited form a high-statistics zero-temperature numerical simulation of the model for two distributions of the random fields, namely a Gaussian and Poissonian distribution, as well as recent advances in finite-size scaling and reweighting methods for disordered systems. An original estimate of the critical slowing down exponent $z$ of the maximum-flow algorithm used is also provided.
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Ising Monte Carlo simulations of the random-field Ising system Fe(0.80)Zn(0.20)F2 are presented for H=10T. The specific heat critical behavior is consistent with alpha approximately 0 and the staggered magnetization with beta approximately 0.25 +- 0.03.
The random-field Ising model (RFIM), one of the basic models for quenched disorder, can be studied numerically with the help of efficient ground-state algorithms. In this study, we extend these algorithm by various methods in order to analyze low-energy excitations for the three-dimensional RFIM with Gaussian distributed disorder that appear in the form of clusters of connected spins. We analyze several properties of these clusters. Our results support the validity of the droplet-model description for the RFIM.
We enlighten some critical aspects of the three-dimensional ($d=3$) random-field Ising model from simulations performed at zero temperature. We consider two different, in terms of the field distributio
The phase diagram of the random field Ising model on the Bethe lattice with a symmetric dichotomous random field is closely investigated with respect to the transition between the ferromagnetic and paramagnetic regime. Refining arguments of Bleher, Ruiz and Zagrebnov [J. Stat. Phys. 93, 33 (1998)] an exact upper bound for the existence of a unique paramagnetic phase is found which considerably improves the earlier results. Several numerical estimates of transition lines between a ferromagnetic and a paramagnetic regime are presented. The obtained results do not coincide with a lower bound for the onset of ferromagnetism proposed by Bruinsma [Phys. Rev. B 30, 289 (1984)]. If the latter one proves correct this would hint to a region of coexistence of stable ferromagnetic phases and a stable paramagnetic phase.
We study magnetic properties of spin glass SG systems under a random field (RF), beased on the suggestion that RFs can be induced by a weak transverse field in the compound LiHo$_x$Y$_{1-x}$F$_4$. We consider a cluster spin model that allows long-range disordered interactions among clusters and short-range interactions inside the clusters, besides a local RF for each spin following a Gaussian distribution with standard deviation $Delta$. We adopt the one-step replica symmetry breaking (RSB) approach to get an exactly solvable single-cluster problem. We discuss the behavior of order parameters, specific heat $C_{m}$, nonlinear susceptibility $chi_3$ and phase diagrams for different disorder configurations. In the absence of RF, the $chi_3$ exhibits a divergence at $T_f$, while the $C_{m}$ shows a broad maximum at a temperature $T^{**}$ around 30$%$ above $T_f$, as expected for conventional SG systems. The presence of RF changes this scenario. The $C_{m}$ still shows the maximum at $T^{**}$ that is weakly dependent on $Delta$. However, the $T_f$ is displaced to lower temperatures, enhancing considerable the ration $T^{**}/T_f$. Furthermore, the divergence in $chi_3$ is replaced by a rounded maximum at a temperature $T^{*}$, which becomes increasingly higher than $T_f$ as $Delta$ enhances. As a consequence, the paramagnetic phase is unfolded in three regions: (i) a conventional paramagnetism ($T>T^{**}$; (ii) a region with formation of short-range order with frozen spins ($T^{*}<T<T^{**}$); (iii) a region with slow growth of free-energy barriers slowing down the spin dynamics before the SG transition ($T_f<T<T^{*}$) suggesting an intermediate Griffiths phase before the SG state. Our results reproduce qualitatively some findings of LiHo$_x$Y$_{1-x}$F$_4$ as the rounded maximum of $chi_3$ behavior triggered by RF.
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