230 research outputs found
Pedestrian Solution of the Two-Dimensional Ising Model
The partition function of the two-dimensional Ising model with zero magnetic
field on a square lattice with m x n sites wrapped on a torus is computed
within the transfer matrix formalism in an explicit step-by-step approach
inspired by Kaufman's work. However, working with two commuting representations
of the complex rotation group SO(2n,C) helps us avoid a number of unnecessary
complications. We find all eigenvalues of the transfer matrix and therefore the
partition function in a straightforward way.Comment: 10 pages, 2 figures; eqs. (101) and (102) corrected, files for fig. 2
fixed, minor beautification
On Duality of Two-dimensional Ising Model on Finite Lattice
It is shown that the partition function of the 2d Ising model on the dual
finite lattice with periodical boundary conditions is expressed through some
specific combination of the partition functions of the model on the torus with
corresponding boundary conditions. The generalization of the duality relations
for the nonhomogeneous case is given. These relations are proved for the
weakly-nonhomogeneous distribution of the coupling constants for the finite
lattice of arbitrary sizes. Using the duality relations for the nonhomogeneous
Ising model, we obtain the duality relations for the two-point correlation
function on the torus, the 2d Ising model with magnetic fields applied to the
boundaries and the 2d Ising model with free, fixed and mixed boundary
conditions.Comment: 18 pages, LaTe
Mean first passage time for fission potentials having structure
A schematic model of over-damped motion is presented which permits one to
calculate the mean first passage time for nuclear fission. Its asymptotic value
may exceed considerably the lifetime suggested by Kramers rate formula, which
applies only to very special, favorable potentials and temperatures. The
additional time obtained in the more general case is seen to allow for a
considerable increment in the emission of light particles.Comment: 7 pages, LaTex, 7 postscript figures; Keywords: Decay rate, mean
first passage tim
Analytical Solution of the Off-Equilibrium Dynamics of a Long Range Spin-Glass Model
We study the non-equilibrium relaxation of the spherical spin-glass model
with p-spin interactions in the limit. We analytically
solve the asymptotics of the magnetization and the correlation and response
functions for long but finite times. Even in the thermodynamic limit the system
exhibits `weak' (as well as `true') ergodicity breaking and aging effects. We
determine a functional Parisi-like order parameter which plays a
similar role for the dynamics to that played by the usual function for the
statics.Comment: 8 pages, Roma preprin
Langevin dynamics with a tilted periodic potential
We study a Langevin equation for a particle moving in a periodic potential in
the presence of viscosity and subject to a further external field
. For a suitable choice of the parameters and the
related deterministic dynamics yields heteroclinic orbits. In such a regime, in
absence of stochastic noise both confined and unbounded orbits coexist. We
prove that, with the inclusion of an arbitrarly small noise only the confined
orbits survive in a sub-exponential time scale.Comment: 38 pages, 6 figure
On the Existence of the Quantum Action
We have previously proposed a conjecture stating that quantum mechanical
transition amplitudes can be parametrized in terms of a quantum action. Here we
give a proof of the conjecture and establish the existance of a local quantum
action in the case of imaginary time in the Feynman-Kac limit (when temperature
goes to zero). Moreover we discuss some symmetry properties of the quantum
action.Comment: revised version, Text (LaTeX
Numerical Stochastic Perturbation Theory for full QCD
We give a full account of the Numerical Stochastic Perturbation Theory method
for Lattice Gauge Theories. Particular relevance is given to the inclusion of
dynamical fermions, which turns out to be surprisingly cheap in this context.
We analyse the underlying stochastic process and discuss the convergence
properties. We perform some benchmark calculations and - as a byproduct - we
present original results for Wilson loops and the 3-loop critical mass for
Wilson fermions.Comment: 35 pages, 5 figures; syntax revise
Influence of the Barrier Shape on Resonant Activation
The escape of a Brownian particle over a dichotomously fluctuating barrier is
investigated for various shapes of the barrier. The problem of resonant
activation is revisited with the attention on the effect of the barrier shape
on optimal value of the mean escape time in the system. The characteristic
features of resonant behavior are analyzed for barriers switching either
between different heights, or "on" and "off" positions. PACS number(s):
05.10-a, 02.50.-r, 82.20.-wj.Comment: 7 pages, 8 figures, RevTex4. Manuscript has been revised and
enhanced. Pictures have been made more clear and some of them have been
cancelled. Additional references have been added. The paper has been
submitted to Phys. Rev.
Experimental Study of Noise-induced Phase Synchronization in Vertical-cavity Lasers
We report the experimental evidence of noise-induced phase synchronization in
a vertical cavity laser. The polarized laser emission is entrained with the
input periodic pump modulation when an optimal amount of white, gaussian noise
is applied. We characterize the phenomenon, evaluating the average frequency of
the output signal and the diffusion coefficient of the phase difference
variable. Their values are roughly independent on different waveforms of
periodic input, provided that a simple condition for the amplitudes is
satisfied. The experimental results are compared with numerical simulations of
a Langevin model
Inattainability of Carnot efficiency in the Brownian heat engine
We discuss the reversibility of Brownian heat engine. We perform asymptotic
analysis of Kramers equation on B\"uttiker-Landauer system and show
quantitatively that Carnot efficiency is inattainable even in a fully
overdamping limit. The inattainability is attributed to the inevitable
irreversible heat flow over the temperature boundary.Comment: 5 pages, to appear in Phys. Rev.
- …