A Contour Method on Cayley tree

We consider a finite range lattice models on Cayley tree with two basic properties: the existence of only a finite number of ground states and with Peierls type condition. We define notion of a contour for the model on the Cayley tree. By a contour argument we show the existence of $s$ different (where $s$ is the number of ground states) Gibbs measures.Comment: 12 page

Context Free Evolution of Words

Projet MEVALRandom grammars were introduced in computer science, but the study of their thermodynamic and long time behaviour started only recently. In this paper we undertake more detailed study of context free grammars in the supercritical case, that is when the word grows exponentially fast. We study and calculate the statistics of factors for large t, prove the existence of various limiting measures and study relations between them

Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models

We use Monte Carlo techniques and analytical methods to study the phase diagram of multicomponent Widom-Rowlinson models on a square lattice: there are M species all with the same fugacity z and a nearest neighbor hard core exclusion between unlike particles. Simulations show that for M between two and six there is a direct transition from the gas phase at z < z_d (M) to a demixed phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In this phase, which is driven by entropy, particles, independent of species, preferentially occupy one of the sublattices, i.e. spatial symmetry but not particle symmetry is broken. The transition at z_d(M) appears to be first order for M \geq 5 putting it in the Potts model universality class. For large M the transition between the crystalline and demixed phase at z_d(M) can be proven to be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to behave as \mu_{cr}/M, with \mu_{cr} the value of the fugacity at which the one component hard square lattice gas has a transition, and to be always of the Ising type. Explicit calculations for the Bethe lattice with the coordination number q=4 give results similar to those for the square lattice except that the transition at z_d(M) becomes first order at M>2. This happens for all q, consistent with the model being in the Potts universality class.Comment: 26 pages, 15 postscript figure

Study of the process e+e−→3(π+π−) in the c.m. energy range 1.5–2.0 GeV with the CMD-3 detector

AbstractThe cross section of the process e+e−→3(π+π−) has been measured using a data sample of 22 pb−1 collected with the CMD-3 detector at the VEPP-2000 e+e− collider. 7956 signal events are selected in the center-of-mass energy range 1.5–2.0 GeV. The measured cross section exhibits a sharp drop near the pp¯ threshold. A first study of dynamics of six-pion production has been performed

Closed system of equations for description of the

We develop a self-consistent kinetic description of a e+e– γ plasma, generated from vacuum in a focal spot of counterpropagating laser pulses. Our model assumes purely time-dependent external (laser) field, but properly takes into account the semiclassical internal (plasma) field, as well as quantum radiation. While nonperturbative kinetic description of e+e–-pair production from vacuum and the simplest variant of backreaction problem have been previously addressed, quantum radiation is included in such a model for the first time. To achieve this goal we derived coupled kinetic equations for the electron, positron, and photon plasma species and the Maxwell equation for the internal electric field. Photon subsystem is included systematically using the BBGKY chain, which we truncate at the second order of perturbation theory by taking into account the annihilation and radiation channels. An important application of our results would be consideration of laser field depletion due to cascade production beyond the locally constant field approximation

Closed system of equations for description of the e+e– γ plasma generated from vacuum by strong electric field

We develop a self-consistent kinetic description of a e+e– γ plasma, generated from vacuum in a focal spot of counterpropagating laser pulses. Our model assumes purely time-dependent external (laser) field, but properly takes into account the semiclassical internal (plasma) field, as well as quantum radiation. While nonperturbative kinetic description of e+e–-pair production from vacuum and the simplest variant of backreaction problem have been previously addressed, quantum radiation is included in such a model for the first time. To achieve this goal we derived coupled kinetic equations for the electron, positron, and photon plasma species and the Maxwell equation for the internal electric field. Photon subsystem is included systematically using the BBGKY chain, which we truncate at the second order of perturbation theory by taking into account the annihilation and radiation channels. An important application of our results would be consideration of laser field depletion due to cascade production beyond the locally constant field approximation

From the seminar on Mathematical Statistical Physics in Moscow State University, 1962–1994. Gibbs random fields on the lattice. Definitions, existence, uniqueness

International audienc

From the seminar on Mathematical Statistical Physics in Moscow State University, 1962–1994. Contour technics

International audienc