New type of extreme value statistics

We investigate the extreme value statistics connected with the dilute Random Energy Model with integer couplings. New universality class is found.Comment: latex, corrected, new universality class is consequence of discreteness of original distributio

Finite size effects in Derrida's model multicriticities and limits of generalization for the Zamolodchikov' s C-theorem

Finite size effects in the multicriticity point and boundaries between phases are calculated. There are anomalous large finite size effects on the boundary of ferromagnetic phase with paramagnetic or spin-glass. Multicriticity point is not giving global minimum for the finite size corrections of free energy.Comment: LaTeX file, 7 pages, no figure

Directed random walks on hierarchic trees with continuous branching: a renormalization group approach

We investigate the directed random walk on hierarchic trees. Two cases are investigated: random variables on deterministic trees with a continuous branching, and random variables on the trees constructed trough the random branching process. We derive renormalization group (partial differential) equations for the branching models with binomial, Poisson and compound Poisson distributions of random variables on the links of tree. These renormaliation group equations are new class of reaction-diffusion equations in 1-dimension.Comment: 6 page

The calculation of multi-fractal properties of directed random walks on hierarchic trees with continuous branching

We consider the hierarchic tree Random Energy Model with continuous branching and calculate the moments of the corresponding partition function. We establish the multifractal properties of those moments. We derive formulas for the normal distribution of random variables, as well as for the general case. We compare our results for the moments of partition function with corresponding results of logarithmic 1-d REM and conjecture a specific power-law tail for the partition function distribution in the high-temperature phase. Our results establish a connection between reaction-diffusion equations and multi-scaling.Comment: 6 pages, 3 figure

8 levels of harmony and 8 concepts of Complex Systems

A set of general physical principles is proposed as the structural basis for the theory of complex systems. First the concept of harmony is analyzed and its different aspects are uncovered. Then the concept of reflection is defined and illustrated by suggestive examples. Later we propose the principle of (random) projection of symmetrically expanded prereality as the main description method of complex systems.Comment: 4 pages, minor corrections in modality principl

Spin glasses at imaginary temperature

We consider spherical p-spin glass and p-spin glass models at imaginary temperatures. Imaginary temperatures are special case, when order parameters are real value numbers. Here there is a some antiferromagnetic like order.Comment: latex, 5 page

Mapping markets to the statistical mechanics: the derivatives act against the self-regulation of stock market

Mapping the economy to the some statistical physics models we get strong indications that, in contrary to the pure stock market, the stock market with derivatives could not self-regulate.Comment: 3 page

Random Energy Model as a paradigm of complex systems

A quadratic extension of REM has been treated. Discussed here is the origin of relation of REM to strings and other complex physical phenomena. Two basic features of the REM class of complex phenomena were identified: the double thermodynamic reflection (a hierarchy of free energies) including the strong reflection at the upper level (the free energy on the order of a logarithm of the degrees of freedom) and the loss (complete or partial) of the local symmetry property. Two main classes of complex phenomena related to REM are seen: the spin glass phase of REM and the boundary the spin glass-ferromagnetic phases. Some examples of physics interest are analyzed from this viewpoint.Comment: latex, The English is correcte

Simplified dynamics for glass model

In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system phenomonologically, as exchange of energy between 2 parts. It is possible to identify trap points in phase space. We suggest some phenomonological approximation-truncated Langevine. The mean field statics is used to introduce a phenomenologic dynamics as its natural extension. Purely kinetical phase transitions are investigated..Comment: revtex, 3 page

Multiscaling at ferromagnetic-spin glass transition point of Random Energy Model and complexity

We calculate moments of free energy's finite size correction for the transition point between ferromagnetic and spin glass phases. We find, that those moments scale with the number of spins with different critical indices, characteristic for the multiscaling. This critical point corresponds to threshold of errorless coding for a gaussian noisy channel. We are give the definition of statistical complexity using this free energy approach.Comment: 9 pages, late