Search results for "Thermodynamic limit"

Ergodicity breaking in a mean field Potts glass: A Monte Carlo investigation

2002

We use Monte Carlo simulations, single spin-flip as well as parallel tempering techniques to investigate the 10-state fully connected Potts glass for system sizes of up to N = 2560. We find that the α-relaxation shows a strong dependence on N and that for the system sizes considered the system remains ergodic even at temperatures below T D , the dynamical critical temperature for this model. However, if one uses the data for the finite size systems, such as the relaxation times or the time dependence of the spin autocorrelation function, and extrapolates them to the thermodynamic limit, one finds that they are indeed compatible with the results for N = ∞ (which are known from analytical cal…

Exact Bethe-ansatz thermodynamics for the sine-Gordon model in the classical limit: Effect of long strings.

1986

Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics

2007

pa href="http://oe.osa.org/virtual_issue.cfm?vid=36"Focus Serial: Frontiers of Nonlinear Optics/a/pThis concise review is aimed at providing an introduction to the kinetic theory of partially coherent optical waves propagating in nonlinear media. The subject of incoherent nonlinear optics received a renewed interest since the first experimental demonstration of incoherent solitons in slowly responding photorefractive crystals. Several theories have been successfully developed to provide a detailed description of the novel dynamical features inherent to partially coherent nonlinear optical waves. However, such theories leave unanswered the following important question: Which is the long term…

Simulation of vapor-liquid coexistence in finite volumes: a method to compute the surface free energy of droplets.

2009

When a fluid at a constant density $\ensuremath{\rho}$ in between the densities of coexisting vapor $({\ensuremath{\rho}}_{\text{v}})$ and liquid $({\ensuremath{\rho}}_{\ensuremath{\ell}})$ at temperatures below criticality is studied in a (cubic) box of finite linear dimension $L$, phase separation occurs in this finite volume, provided $L$ is large enough. For a range of densities, one can observe a liquid droplet (at density ${\ensuremath{\rho}}_{\ensuremath{\ell}}^{\ensuremath{'}}$ slightly exceeding ${\ensuremath{\rho}}_{\ensuremath{\ell}}$) coexisting in stable thermal equilibrium with surrounding vapor (with density ${\ensuremath{\rho}}_{\text{v}}^{\ensuremath{'}}g{\ensuremath{\rho}}…

?Almost? mean-field ising model: An algebraic approach

1991

We study the thermodynamic limit of the algebraic dynamics for an "almost" mean-field Ising model, which is a slight generalization of the Ising model in the mean-field approximation. We prove that there exists a family of "relevant" states on which the algebraic dynamics αt can be defined. This αt defines a group of automorphisms of the algebra obtained by completing the standard spin algebra with respect to the quasiuniform topology defined by our states. © 1991 Plenum Publishing Corporation.

What is the order of the two-dimensional polymer escape transition?

2007

An end-grafted flexible polymer chain in three-dimensional space between two pistons undergoes an abrupt transition from a confined coil to a flowerlike conformation when the number of monomers in the chain, $N$, reaches a critical value. In two-dimensional (2D) geometry, excluded-volume interactions between monomers of a chain confined inside a strip of finite length $2L$ transform the coil conformation into a linear string of blobs. However, the blob picture raises questions about the nature of this escape transition. To check theoretical predictions based on the blob picture we study 2D single-polymer chains with excluded-volume interactions and with one end grafted in the middle of a st…

Simulation of Phase Transitions of Single Polymer Chains: Recent Advances

2006

The behaviour of a flexible polymer chain in solvents of variable quality in dilute solution is discussed both in the bulk and in the presence of an adsorbing wall. Monte Carlo simulations of coarse-grained bead-spring models and of the bond fluctuation model are presented and interpreted in terms of phenomenological theories and scaling concepts. Particular attention is paid to the behaviour of the polymer chain when the temperature of the polymer solution gets lower than the Theta temperature. It is argued that the adsorption transition line at the Theta temperature splits into lines of wetting and drying transitions of polymer globules attached to the wall. In addition, it is shown that …

The phase diagram of a single polymer chain: New insights from a new simulation method

2006

We present simulation results for the phase behavior of a single chain for a flexible lattice polymer model using the Wang-Landau sampling idea. Applying this new algorithm to the problem of the homopolymer collapse allows us to investigate not only the high temperature coil–globule transition but also an ensuing crystallization at lower temperature. Performing a finite size scaling analysis on the two transitions, we show that they coincide for our model in the thermodynamic limit corresponding to a direct collapse of the random coil into the crystal without intermediate coil–globule transition. As a consequence, also the many chain phase diagram of this model can be predicted to consist o…

New Results on the Collapse Transition(s) of Flexible Homopolymers

2007

We analyze the collapse transition of flexible homopolymer chains in the bond-fluctuation model employing the Wang-Landau Monte Carlo algorithm. The coil-globule transition is followed by a first order transition into a solid state occurring in the collapsed globule. In the thermodynamic limit (chain length to infinity) the topology of the phase diagram depends on the range of the attractive interaction between the monomers. For sufficiently large interaction range a normal behaviour of a continuous coil-globule transition at the Θ-temperature followed by a crystallization transition at lower temperature is observed. For short interaction range the first-order transition asymptotically can …

Asymptotic analysis of the form-factors of the quantum spin chains

2020

Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic, of the correlation function is one of the most important subject of the theory of the quantum integrable models. In this context an approach based on the calculation of form factors has been proved to be a more effective one. In this thesis, we develop a new method based on the algebraic Bethe ansatz is proposed for the computation of the form-factors in thermodynamic limit. It is applied to and described in the context of isotropic XXX Heisenberg chain, w…