Efficient simulation scheme for studying spin-glass transitions

Barbara Coluzzi B, Preprint Roma N

We study the 4d Heisenberg spin glass model with Gaussian nearestneighbor interactions. We use finite size scaling to analyze the data. We find a behavior consistent with a finite temperature spin glass transition. Our estimates for the critical exponents agree with the results from "-expansion. PACS Numbers 7510N-0270 Preprint Roma1 n o 1054 The lower critical dimension d l of the short range models remains one of the most controversial questions in the spin glass [1]-[3] theory. In the last ten years a consistent number of works has been devoted to studying the Ising model, which seems to be [4, 5] very close to d l in d = 3. In the case of the short range isotropic Heisenberg spin glass, the conclusions of various computer simulations in d = 3 [6, 7] agree that the system is below d l . Using domain wall renormalization group techniques, it was argued [2, 3] that d l = 4 for this model. To our knowledge, there are no previous numerical simulations on the 4d Heisenberg spin glass...

Anonymous

Chengwei Liu

Phase transitions and their associated critical phenomena are of fundamental importance and play a crucial role in the development of statistical physics for both classical and quantum systems. Phase transitions embody diverse aspects of physics and also have numerous applications outside physics, e.g., in chemistry, biology, and combinatorial optimization problems in computer science. Many problems can be reduced to a system consisting of a large number of interacting agents, which under some circumstances (e.g., changes of external parameters) exhibit collective behavior; this type of scenario also underlies phase transitions. The theoretical understanding of equilibrium phase transitions was put on a solid footing with the establishment of the renormalization group. In contrast, non-equilibrium phase transition are relatively less understood and currently a very active research topic. One important milestone here is the Kibble-Zurek (KZ) mechanism, which provides a useful framework for describing a system with a transition point approached through a non-equilibrium quench process. I developed two efficient Monte Carlo techniques for studying phase transitions, one is for classical phase transition and the other is for quantum phase transitions, both are under the framework of KZ scaling. For classical phase transition, I develop a non-equilibrium quench (NEQ) simulation that can completely avoid the critical slowing down problem. For quantum phase transitions, I develop a new algorithm, named quasi-adiabatic quantum Monte Carlo (QAQMC) algorithm for studying quantum quenches. I demonstrate the utility of QAQMC quantum Ising model and obtain high-precision results at the transition point, in particular showing generalized dynamic scaling in the quantum system. To further extend the methods, I study more complex systems such as spin-glasses and random graphs. The techniques allow us to investigate the problems efficiently. From the classical perspective, using the NEQ approach I verify the universality class of the 3D Ising spin-glasses. I also investigate the random 3-regular graphs in terms of both classical and quantum phase transitions. I demonstrate that under this simulation scheme, one can extract information associated with the classical and quantum spin-glass transitions without any knowledge prior to the simulation.

Yukiyasu Ozeki, Nobuyasu Ito, 尾関 之康 +1 more

I. Morgenstern

Arnab Das, Bikas K. Chakrabarti

Here we discuss the annealing behavior of an infinite-range +/-J Ising spin glass in the presence of a transverse field using a zero-temperature quantum Monte Carlo method. Within the simulation scheme, we demonstrate that quantum annealing not only helps finding the ground state of a classical spin glass, but can also help simulating the ground state of a quantum spin glass, in particular, when the transverse field is low, much more efficiently.