Modern Physics Letters B

The present review is devoted to the problems of finite-size scaling due to the presence of long-range interaction decaying at large distance as 1/r^d+σ, σ>0. The attention is focused mainly on the renormalization group results in the framework of -theory for systems with fully finite (block) geometry under periodic boundary conditions. Some bulk critical properties and Monte Carlo results are also reviewed. The role of the cut-off effects as well as their relation with those originating from the long-range interaction is additionally discussed. Special attention is paid to the description of an adequate mathematical technique that allows for the treatment of the long-range and short-range interactions equally. The review concludes with a short discussion of some open problems.

The Bessel equation is shown to be equivalent, under suitable transformations, to a system of two damped/amplified parametric oscillator equations, which have been used in the study of inflationary models of the Universe, thermal field theories and Chern–Simons gauge theories. The breakdown of loop-antiloop symmetry due to group contraction manifests itself as breaking of time-reversal symmetry. The relation between some infinite dimensional loop-algebras, such as the Virasoro-like algebra, and the Euclidean algebras e(2) and e(3) is also analyzed.

We derive the canonical distribution as a stationary solution of the Liouville equation for the classical dissipative system. Dissipative classical systems can have stationary states that look like canonical Gibbs distributions. The condition for non-potential forces which leads to this stationary solution is very simple: the power of the non-potential forces must be directly proportional to the velocity of the Gibbs phase (phase entropy density) change. The example of the canonical distribution for a linear oscillator with friction is considered.

The short-time critical behavior of the random n-vector model with long-range interaction is studied by the theoretic renormalization-group approach. After a sudden quench to the critical temperature from the high temperature phase, the system is released to an evolution within model A dynamics. The initial slip exponents and the dynamic exponent are calculated to two-loop order.

We give a path-integral argument to obtain the classical regime of a quantum system by means of an external magnetic random field.

xProtein folding in a two-dimensional lattice with an unrestricted boundary is simulated by means of the simplified HP model. The proteins are regarded as peptide chains and fold into compact structures. These structures are classified by the number of core sites. It is found that the number of structures with the given designability and given number of core sites versus designability appears as the normal distribution. The simulation shows that the structures with a large number of core sites have a high designability.