We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of fourfold coordinated sites connected via variable length one-dimensional chains. Our emphasis is on nonuniversal properties and we consider the transition temperature and other equilibrium thermodynamic properties, including those associated with one-dimensional fluctuations arising from the chains. We use analytic methods in the annealed case, and a Monte Carlo simulation for the quenched disorder. Our objective is to study the difference between quenched and annealed results with a broad random distribution of interaction parameters. The former represents a situation where the time scale associated with the randomness is very long and the corresponding degrees of freedom can be viewed as frozen, while the annealed case models the situation where this is not so. We find that the transition temperature and the entropy associated with one-dimensional fluctuations are always higher for quenched disorder than in the annealed case. These differences increase with the strength of the disorder up to a saturating value. We discuss our results in connection to physical systems where a broad distribution of interaction strengths is present.
We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of fourfold coordinated sites connected via variable length one-dimensional chains. Our emphasis is on nonuniversal properties and we consider the transition temperature and other equilibrium thermodynamic properties, including those associated with one-dimensional fluctuations arising from the chains. We use analytic methods in the annealed case, and a Monte Carlo simulation for the quenched disorder. Our objective is to study the difference between quenched and annealed results with a broad random distribution of interaction parameters. The former represents a situation where the time scale associated with the randomness is very long and the corresponding degrees of freedom can be viewed as frozen, while the annealed case models the situation where this is not so. We find that the transition temperature and the entropy associated with one-dimensional fluctuations are always higher for quenched disorder than in the annealed case. These differences increase with the strength of the disorder up to a saturating value. We discuss our results in connection to physical systems where a broad distribution of interaction strengths is present.
We investigate equilibrium statistical properties of the isotropic quantum XY spin-1/2 model in an external magnetic field when the interaction and field parts are subjected to quenched or annealed disorder or both. The randomness present in the system are termed annealed or quenched depending on the relation between two different time scales---the time scale associated with the equilibration of the randomness and the time of observation. Within a mean-field framework, we study the effects of disorders on spontaneous magnetization, both by perturbative and numerical techniques. Our primary interest is to understand the differences between quenched and annealed cases, and also to investigate the interplay when both of them are present in a system. We find that the magnetization survives in the presence of a unidirectional random field, irrespective of its nature, i.e., whether it is quenched or annealed. However, the field breaks the circular symmetry of the magnetization, and the system magnetizes in specific directions, parallel or transverse to the applied magnetic field. Interestingly, while the transverse magnetization is affected by the annealed disordered field, the parallel one remains unfazed by the same. Moreover, the annealed disorder present in the interaction term does not affect the system's spontaneous magnetization and the corresponding critical temperature, irrespective of the presence or absence of quenched or annealed disorder in the field term. We carry out a comparative study of these and all other different combinations of the disorders in the interaction and field terms, and point out their generic features.
The effect of a discrete distribution of annealed random fields on the properties of the two-dimensional Ising model is studied. The random field is allowed to assume the values 0,\ifmmode\pm\else\textpm\fi{}h with the probabilities p0,${p}_{\ifmmode\pm\else\textpm\fi{}}$, and a parameter \ensuremath{\mu} is introduced which is determined by specifying p0. Exact results are obtained by mapping the model onto an effective Ising model on the rectangular lattice without field, and the probabilities p0,${p}_{\ifmmode\pm\else\textpm\fi{}}$ are expressed in terms of the magnetization and two-spin correlations of the effective model. It is shown that the long-range order is not destroyed by the random field and the transition temperature increases as p0 decreases. For a given p0 the critical temperature increases with the field strength and these combined effects show that the annealed random field favors the ordering of the system, therefore presenting behavior opposite to that expected for the system in a quenched random field.
We study the two-dimensional Ising model on networks with quenched topological (connectivity) disorder. In particular, we construct random lattices of constant coordination number and perform large-scale Monte Carlo simulations in order to obtain critical exponents using finite-size scaling relations. We find disorder-dependent effective critical exponents, similar to diluted models, showing thus no clear universal behavior. Considering the very recent results for the two-dimensional Ising model on proximity graphs and the coordination number correlation analysis suggested by Barghathi and Vojta [Phys. Rev. Lett. 113, 120602 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.120602], our results indicate that the planarity and connectedness of the lattice play an important role on deciding whether the phase transition is stable against quenched topological disorder.
In this work, we simulated a quenched random mixed-spin Ising model on the square lattice. The model system consists of two different particles with spins σ = 1/2 (states ±1/2) and S = 1 (states ±1, 0). These particles are randomly distributed on the lattice, and we considered only nearest-neighbor interactions. This model can represent a random magnetic binary alloy AxB1-x, obtained from the high-temperature quenching of a liquid mixture. We performed Monte Carlo simulations for several lattice sizes and temperatures, and we found its critical temperature through the reduced fourth-order cumulant. We also determined the magnetization, the susceptibility, and the specific heat as a function of temperature. We used finite-size scaling arguments to estimate the critical exponents β, γ, and ν of the model. We showed that the quenched model is in the same universality class of the two-dimensional pure Ising model. We also investigated the sample to sample fluctuations that occur in the values of the thermodynamic quantities in order to describe the self-averaging properties at the critical point.
A study of the influence of different types of disorder on systems in the Ising universality class by employing both a dynamical field theory approach and extensive Monte Carlo simulations is presented. We reproduce some well-known results for the case of quenched disorder (random temperature and random field), and analyze the effect of four different types of time-dependent disorder scarcely studied so far in the literature. Some of them are of obvious experimental and theoretical relevance (as, for example, globally fluctuating temperatures or random fields). All the predictions coming from our field-theoretical analysis are fully confirmed by extensive simulations in two and three dimensions, and novel qualitatively different, non-Ising transitions are reported. Possible experimental setups designed to explore the described phenomenologies are also briefly discussed.
PACS. 05.10.Cc – Renormalization group methods. PACS. 64.60.-i – General studies of phase transitions. PACS. 75.10.Hk – Classical spin models. Abstract. – A study of the influence of different types of disorder on systems in the Ising universality class by employing both a dynamical field theory approach and extensive Monte Carlo simulations is presented. We reproduce some well-known results for the case of quenched disorder (random temperature and random field), and analyze the effect of four different types of time-dependent disorder scarcely studied so far in the literature. Some of them are of obvious experimental and theoretical relevance (as, for example, globally fluctuating temperatures or random fields). All the predictions coming from our field-theoretical analysis are fully confirmed by extensive simulations in two and three dimensions, and novel qualitatively different, non-Ising transitions are reported. Possible experimental setups designed to explore the described phenomenologies are also briefly discussed. The Ising model has played a central role in the development of modern statistical mechanics. Its universality class includes a broad variety of models and real materials, as magnetic