On products of skew rotations

Let $H_1(p,q)$, $H_2(p,q)$ be two time-independent Hamiltonians with one degree of freedom and $\{S_1^t\}$, $\{S_2^t\}$ be the one-parametric groups of shifts along the orbits of Hamiltonian systems generated by $H_1$, $H_2$. In some problems of population genetics there appear the transformations of the plane having the form $T^{(h_1,h_2)}=S^{h_2}_2\cdot S_1^{h_1}$ under some conditions on $H_1$, $H_2$. We study in this paper asymptotical properties of trajectories of $T^{(h_1,h_2)}$.Comment: 13 pages, 10 figure

Multi-frequency Studies of Massive Cores with Complex Spatial and Kinematic Structures

Five regions of massive star formation have been observed in various molecular lines in the frequency range $\sim 85-89$ GHz. The studied regions possess dense cores, which host young stellar objects. The physical parameters of the cores are estimated, including kinetic temperatures ($\sim 20-40$ K), sizes of the emitting regions ($\sim 0.1-0.6$ pc), and virial masses ($\sim 40-500 M_{\odot}$). Column densities and abundances of various molecules are calculated in the local thermodynamical equilibrium approximation. The core in 99.982+4.17, associated with the weakest IRAS source, is characterized by reduced molecular abundances. Molecular line widths decrease with increasing distance from the core centers ($b$). For b\ga 0.1~pc, the dependences $\Delta V(b)$ are close to power laws ($\propto b^{-p}$), where $p$ varies from $\sim 0.2$ to $\sim 0.5$, depending on the object. In four cores, the asymmetries of the optically thick HCN(1--0) and HCO$^+$(1--0) lines indicate systematic motions along the line of sight: collapse in two cores and expansion in two others. Approximate estimates of the accretion rates in the collapsing cores indicate that the forming stars have masses exceeding the solar mass.Comment: 18 pages, 7 figures, 6 table

Rigorous Analysis of Singularities and Absence of Analytic Continuation at First Order Phase Transition Points in Lattice Spin Models

We report about two new rigorous results on the non-analytic properties of thermodynamic potentials at first order phase transition. The first one is valid for lattice models ($d\geq 2$) with arbitrary finite state space, and finite-range interactions which have two ground states. Under the only assumption that the Peierls Condition is satisfied for the ground states and that the temperature is sufficiently low, we prove that the pressure has no analytic continuation at the first order phase transition point. The second result concerns Ising spins with Kac potentials $J_\gamma(x)=\gamma^d\phi(\gamma x)$, where $0<\gamma<1$ is a small scaling parameter, and $\phi$ a fixed finite range potential. In this framework, we relate the non-analytic behaviour of the pressure at the transition point to the range of interaction, which equals $\gamma^{-1}$. Our analysis exhibits a crossover between the non-analytic behaviour of finite range models ($\gamma>0$) and analyticity in the mean field limit ($\gamma\searrow 0$). In general, the basic mechanism responsible for the appearance of a singularity blocking the analytic continuation is that arbitrarily large droplets of the other phase become stable at the transition point.Comment: 4 pages, 2 figure

Critical droplets in Metastable States of Probabilistic Cellular Automata

We consider the problem of metastability in a probabilistic cellular automaton (PCA) with a parallel updating rule which is reversible with respect to a Gibbs measure. The dynamical rules contain two parameters $\beta$ and $h$ which resemble, but are not identical to, the inverse temperature and external magnetic field in a ferromagnetic Ising model; in particular, the phase diagram of the system has two stable phases when $\beta$ is large enough and $h$ is zero, and a unique phase when $h$ is nonzero. When the system evolves, at small positive values of $h$, from an initial state with all spins down, the PCA dynamics give rise to a transition from a metastable to a stable phase when a droplet of the favored $+$ phase inside the metastable $-$ phase reaches a critical size. We give heuristic arguments to estimate the critical size in the limit of zero ``temperature'' ($\beta\to\infty$), as well as estimates of the time required for the formation of such a droplet in a finite system. Monte Carlo simulations give results in good agreement with the theoretical predictions.Comment: 5 LaTeX picture

One Step Non SUSY Unification

We show that it is possible to achieve one step gauge coupling unification in a general class of non supersymmetric models which at low energies have only the standard particle content and extra Higgs fields doublets. The constraints are the experimental values of $\alpha_{em}$, $\alpha_s$ and $\sin^2\theta_W$ at $10^2 GeVs$, and the lower bounds for FCNC and proton decay rates. Specific example are pointed out.Comment: 10 pages, Latex file,, uses epsf style, Two Postscript figures included. To appear in Europhysics Letter

Mean-field driven first-order phase transitions in systems with long-range interactions

We consider a class of spin systems on $\Z^d$ with vector valued spins (\bS_x) that interact via the pair-potentials J_{x,y} \bS_x\cdot\bS_y. The interactions are generally spread-out in the sense that the $J_{x,y}$'s exhibit either exponential or power-law fall-off. Under the technical condition of reflection positivity and for sufficiently spread out interactions, we prove that the model exhibits a first-order phase transition whenever the associated mean-field theory signals such a transition. As a consequence, e.g., in dimensions $d\ge3$, we can finally provide examples of the 3-state Potts model with spread-out, exponentially decaying interactions, which undergoes a first-order phase transition as the temperature varies. Similar transitions are established in dimensions $d=1,2$ for power-law decaying interactions and in high dimensions for next-nearest neighbor couplings. In addition, we also investigate the limit of infinitely spread-out interactions. Specifically, we show that once the mean-field theory is in a unique ``state,'' then in any sequence of translation-invariant Gibbs states various observables converge to their mean-field values and the states themselves converge to a product measure.Comment: 57 pages; uses a (modified) jstatphys class fil

General Theory of Lee-Yang Zeros in Models with First-Order Phase Transitions

We present a general, rigorous theory of Lee-Yang zeros for models with first-order phase transitions that admit convergent contour expansions. We derive formulas for the positions and the density of the zeros. In particular, we show that for models without symmetry, the curves on which the zeros lie are generically not circles, and can have topologically nontrivial features, such as bifurcation. Our results are illustrated in three models in a complex field: the low-temperature Ising and Blume-Capel models, and the $q$-state Potts model for $q$ large enough.Comment: 4 pgs, 2 figs, to appear in Phys. Rev. Let

A crystallographic phase transition within the magnetically ordered state of Ce_2Fe_17

X-ray diffraction experiments were performed on polycrystalline and single-crystal specimens of Ce$_{2}$Fe$_{17}$ at temperatures between 10 K and 300 K. Below $T_{\mathrm{t}}$ = 118$\pm$2 K, additional weak superstructure reflections were observed in the antiferromagnetically ordered state. The superstructure can be described by a doubling of the chemical unit cell along the $\mathbf{c}$ direction in hexagonal notation with the same space group $R \bar{3} m$ as the room-temperature structure. The additional antiferromagnetic satellite reflections observed in earlier neutron diffraction experiments can be conclusively related to the appearance of this superstructure.Comment: 8 pages, figures, submitted for publication in Phys. Rev.

Magnetism of ordered and disordered alloys of R2Fe14B (R = Nd, Er) type

Magnetic susceptibility, magnetization and neutron diffraction measurements have been performed to study structure and magnetic states of crystalline and amorphous Nd2Fe14B and Er2Fe14B alloys. In the crystalline state there exists a large (about 20%) anisotropy of Er-sublattice magnetization. Values of the magnetic anisotropy constant of Er ions and the Er-Fe exchange-coupling parameter were estimated using temperature dependence of the Er-and Fe-sublattice magnetizations. Amorphous state of the samples was obtained by irradiation of fast (Eeff≥1MeV) neutrons with a fluence up to the 1.2 Ч 1020 n/cm-2 at 340 K. It is shown that antiferromagnetic coupling between the rare-earth and iron spins is kept in the amorphous state. Amorphization of the samples is found to result in reduction of the Curie temperature (TC) by about 200 K and almost total absence of coercivity. We suggest that the strong decrease of TC is a consequence of enhancement of negative Fe-Fe interactions as a result of dispersion of interatomic distances, which is a characteristic feature of the amorphous state. © 2013 Elsevier B.V. All rights reserved