
Monte Carlo simulations in statistical physics
Allocation
Abstract
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 NPhard. 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 [1],
to the Ising spin glass (aka the EdwardsAnderson 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
offlattice 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.
[1] Jack Lidmar, Phys. Rev. E 85, 056708 (2012).
