Research into Various Exact and Numerical Aspects .. (RAVEN)
Research into Various Exact and Numerical Aspects of Critical Phenomena
Start date: Apr 1, 2013,
End date: Mar 31, 2015
"A cornerstone in the study of phase transitions is the principal of universality. This maintains that entire families of systems behave identically in the neighbourhood of criticality, such as the transition point between a liquid and a gas or at the Curie point in a magnet, at which two phases become indistinguishable. Near the critical point, thermodynamic observables and critical exponents do not depend on the details of intermolecular interactions. Instead they depend only on the range of interactions, symmetries and spatial dimensionality. This fact allows us to understand real materials and systems through simplified mathematical models.The universality concept is commonly stated together with the hypotheses of scaling and finite-size scaling. The associated theories have been mostly successful in describing critical and non-critical properties, but significant discrepancies between them and experiments remain. To understand the experiments, the theories have to be improved. This project seeks to increase our understanding by researching corrections to scaling. Our proposal is to investigate statistical mechanical models in an attempt to place our theoretical understanding of critical phenomena closer on firmer ground and to render them closer to experimental measurements.We will especially target universality, scaling, and finite-size effects in two dimensional models of statistical mechanics as these can be tackled using exact methods, as well as analytic and numerical ones. In addition, more challenging three dimensional models will be investigated.Theories of critical phenomena in particular are crucial in our understanding of how everything depends on everything else in many disciplines outside physics. It thus permeates all of natural sciences and even beyond. It is therefore a priority that this foundation stone be correct, exact and fully understood."
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