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

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

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

Imitation of 2d quantum field theory by means of REM like models

An imitation of 2d field theory is formulated by means of a model on the hierarchic tree (with branching number close to one) with the same potential and the free correlators identical to those of 2d ones. Such a model possesses some features of original models for certain scale invariant theories. For the case of 2d conformal models it is possible to derive exact results. The renormalization group equation for the free energy is a reaction-diffusion equation, which is noise-free KPZ equation with an additional linear term. For the case of Liouville model and strings these models on trees may be naturally expressed via the Random Energy Model. This correspondence is used to identify the phase structure of strings for analytical continuation of DDK expressions. A phase transition is found for spherical strings a bit below three dimensions.Comment: latex, 17 page

The harmony, reflection and other principles 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: 11 pages,latex, more examples are added to the tex

Multi-access channels in quantum information theory

The multi-access channels in quantum information theory are considered. Classical messages from independent sources, which are represented as some quantum states, are transported by a channel to one address. The messages can interact with each other and with external environment. After statement of problem and proving some general results we investigate physically important case when information is transported by states of electromagnetic field. One-way communication by noisy quantum channels is also considered.Comment: LaTex file, 12 page

Finite Size Effects for the Dilute Coupling Derrida Model

We consider paramagnetic, spin-glass and ferromagnetic phases. At $T=0$ model gives for the some values of connectivity (near the critical) extremal suppression of finite size effects (decoding error probability).Comment: LaTeX file, 13 pages, acknowledgments are correcte