Search results for "Mathematical physics"
showing 10 items of 2687 documents
Statistical mechanics of the NLS models and their avatars
2006
“In Vishnuland what avatar? Or who in Moscow (Leningrad) towards the czar [1]”. The different manifestations (avatars) of the Nonlinear Schrodinger equation (NLS models) are described including both classical and quantum integrable cases. For reasons explained the sinh-Gordon and sine-Gordon models, which can be interpreted as covariant manifestations of the ‘repulsive’ and ‘attractive’ NLS models, respectively, are chosen as generic models for the statistical mechanics. It is shown in the text how the quantum and classical free energies can be calculated by a method of functional integration which uses the classical action-angle variables on the real line with decaying boundary conditions,…
Dynamic percolation transition induced by phase separation: A Monte Carlo analysis
1987
The percolation transition of geometric clusters in the three-dimensional, simple cubic, nearest neighbor Ising lattice gas model is investigated in the temperature and concentration region inside the coexistence curve. We consider “quenching experiments,” where the system starts from an initially completely random configuration (corresponding to equilibrium at infinite temperature), letting the system evolve at the considered temperature according to the Kawasaki “spinexchange” dynamics. Analyzing the distributionnl(t) of clusters of sizel at timet, we find that after a time of the order of about 100 Monte Carlo steps per site a percolation transition occurs at a concentration distinctly l…
Localization at low temperature and infrared bounds
2006
We consider a class of classical lattice spin systems, with Rn-valued spins and two-body interactions. Our main result states that the associated Gibbs measure localizes in certain cylindrical neighborhoods of the global minima of the unperturbed Hamiltonian. As an application we establish existence of a first order phase transition at low temperature, for a reflection positive mexican hat model on Zd, d⩾3, with a nonferromagnetic interaction.
Monte Carlo simulation of phase separation and clustering in the ABV model
1991
As a model for a binary alloy undergoing an unmixing phase transition, we consider a square lattice where each site can be either taken by an A atom, a B atom, or a vacancy (V), and there exists a repulsive interaction between AB nearest neighbor pairs. Starting from a random initial configuration, unmixing proceeds via random jumps of A atoms or B atoms to nearest neighbor vacant sites. In the absence of any interaction, these jumps occur at jump ratesΓ A andΓ B, respectively. For a small concentration of vacancies (c v=0.04) the dynamics of the structure factorS(k,t) and its first two momentsk 1(t),k 2 2 (t) is studied during the early stages of phase separation, for several choices of co…
Finite-size scaling for a first-order transition where a continuous symmetry is broken: The spin-flop transition in the three-dimensional XXZ Heisenb…
2019
Finite-size scaling for a first-order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological ``degeneracy'' factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, $XXZ$ Heisenberg antiferromagnet in a field in order to study the finite-size behavior on a $L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L$ simple cubic lattice for the first-order ``spin-flop'' transition between the Ising-like antiferromagnetic state and the canted, $XY$-like state. Our theory predicts that for large linear dimension $L$ the field dependen…
Scaling Behavior of the 2D XY Model Revisited
1998
Using two sets of high-precision Monte Carlo data for the two-dimensional XY model in the Villain formulation on square L × L lattices, the scaling behavior of the susceptibility χ and correlation length ξ in the vicinity of the Kosterlitz-Thouless phase transition is analyzed with emphasis on multiplicative logarithmic corrections (ln ξ)-2r in the high-temperature phase and (ln L)-2r in the finite-size scaling region, respectively.
Corner contribution to cluster numbers in the Potts model
2013
For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N_Gamma of clusters that intersect a given contour Gamma. To leading order, N_Gamma is proportional to the length of the curve. Additionally, however, there occur logarithmic contributions related to the corners of Gamma. These are found to be universal and their size can be calculated employing techniques from conformal field theory. For the Fortuin-Kasteleyn clusters relevant to the thermal phase transition we find agreement with these predictions from large-scale numerical simulations. For the spin clusters, on the other hand, the cluster numbers are no…
Surface effects on phase transitions of modulated phases and at Lifshitz points: A mean field theory of the ANNNI model
1999
The semi-infinite axial next nearest neighbor Ising (ANNNI) model in the disordered phase is treated within the molecular field approximation, as a prototype case for surface effects in systems undergoing transitions to both ferromagnetic and modulated phases. As a first step, a discrete set of layerwise mean field equations for the local order parameter mn in the nth layer parallel to the free surface is derived and solved, allowing for a surface field H1 and for interactions JS in the surface plane which differ from the interactions J0 in the bulk, while only in the z-direction perpendicular to the surface competing nearest neighbor ferromagnetic exchange (J1) and next nearest neighbor an…
Critical behavior of active Brownian particles
2017
We study active Brownian particles as a paradigm for a genuine nonequilibrium phase transition requiring steady driving. Access to the critical point in computer simulations is obstructed by the fact that the density is conserved. We propose a method based on arguments from finite-size scaling to determine critical points and successfully test it for the two-dimensional (2D) Ising model. Using this method allows us to accurately determine the critical point of two-dimensional active Brownian particles at ${\mathrm{Pe}}_{\text{cr}}=40(2), {\ensuremath{\phi}}_{\text{cr}}=0.597(3)$. Based on this estimate, we study the corresponding critical exponents $\ensuremath{\beta}, \ensuremath{\gamma}/\…
Comparison of Silicon Photomultiplier Characteristics using Automated Test Setups
2016
Silicon Photomultipliers (SiPM) are photo-sensors consisting of an array of hundreds to thousands pixels with a typical pitch of 10-100 μm. They exhibit an excellent photon counting and time resolution. Therefore applications of SiPMs are emerging in many fields. In order to characterize SiPMs, the PRISMA Detector Lab at Mainz has established three automated test setups. Setup-A is dedicated to measure the gain, the dark count rate and the optical crosstalk probability. The temperature dependencies are characterized by operating the setup in a climate chamber. Setup-B is an optical system to measure the photon detection efficiency. Setup-C addresses the most challenging aspect of comparing …