Monte Carlo simulations in statistical physics
A variety of different important problems in condensed matter and statistical physics are being studied using large scale computer simulations. In particular effects of disorder, fluctuations, and topological defects on phases and phase transitions, the competition between different kinds of orders, and quantum mechanical effects are important to understand. These problems occur in several different systems, e.g., in random magnets, superconductors, biological physics, etc. Computer simulations are indispensable to study these problems. Disordered systems, such as spin glasses, belong to the most difficult problems and our understanding of these is severely lacking in many respects. The disorder in these systems cause frustration and a very rugged energy landscape with many metastable minima. This leads to a very slow equilibration and interesting dynamical properties, but require very large simulations. The problem of finding the ground state of, e.g., an Ising spin glass is NP-hard. Other examples, with similar rough energy landscapes, include the problem of finding the folded structure of a proteins and other biopolymers. All this make these problems very challenging even for large scale simulations, but recent advancement in algorithms allows for more efficient sampling in such systems. In particular, we employ a recently developed method, the Accelerated Weight Histogram method , to the Ising spin glass (aka the Edwards-Anderson model). One goal here is to calculate the free energy cost of low energy excitations in the glass phase, and how this depends on temperature as the glass transition is approached. This requires very accurate calculations of free energy differences, quite nontrivial in any Monte Carlo simulation, but which our method provides. These free energy differences must then be averaged over thousands of different disorder realisations. We also plan to systematically investigate problems with nontrivial spatial correlations of the disorder. This is a variation of the problem where little is known and the potential for interesting new effects is clear. Such nontrivial correlations are common in nature due to natural or artificial occurrence of electronic or density correlations on nanoscale. For example, such correlations occur naturally in porous media that we intend to investigate. A related problem which has attracted enormous attention in the past years is helium fluids in constrained geometries. Here we intend to systematically study off-lattice path integral simulation of helium atoms to investigate both equilibrium and nonequilibrium properties of helium transport related to recent intriguing experiments. We also plan to continue our long term study of path integral simulations of bosons with disorder to investigate quantum critical dynamics that is a currently debated topic, as well as investigating the possibility to overcome certain sometimes quite limiting approximations that are often used in the simulated models of quantum critical phenomena. Another goal is to use these simulations as a test bench for further development and refinement of the methods and algorithms, and their application to other problems. Of interest is e.g., how to parallelize the method in an optimal way.  Jack Lidmar, Phys. Rev. E 85, 056708 (2012).