923 research outputs found
Finite-Size Scaling on the Ising Coexistence Line
We study the finite-size scaling of moments of the magnetization in the
low-temperature phase of the two-dimensional Ising model.Comment: talk at Lattice '92, 4 pages, Latex, needs espcrc2.sty, figures not
included, CERN-TH.6724/9
Instantons and Surface Tension at a First-Order Transition
We study the dynamics of the first order phase transition in the two
dimensional 15-state Potts model, both at and off equilibrium. We find that
phase changes take place through nucleation in both cases, and finite volume
effects are described well through an instanton computation. Thus a dynamical
measurement of the surface tension is possible. We find that the order-disorder
surface tension is compatible with perfect wetting. An accurate treatment of
fluctuations about the instanton solution is seen to be of great importance.Comment: HLRZ 65/93 [plain TeX, 10 pages including 3 ps figures.
Finite size scaling analysis of compact QED
We describe results of a high-statistics finite size scaling analysis of 4d
compact U(1) lattice gauge theory with Wilson action at the phase transition
point. Using a multicanonical hybrid Monte Carlo algorithm we generate data
samples with more than 150 tunneling events between the metastable states of
the system, on lattice sizes up to 18^4. We performed a first analysis within
the Borgs-Kotecky finite size scaling scheme. As a result, we report evidence
for a first-order phase transition with a plaquette energy gap, G=0.02667(20),
at a transition coupling, beta_T=1.011128(11).Comment: Lattice 2000 (Topics in Gauge Theories),6 pages, 6 figures, LaTe
Finite Size Scaling Analysis with Linked Cluster Expansions
Linked cluster expansions are generalized from an infinite to a finite volume
on a -dimensional hypercubic lattice. They are performed to 20th order in
the expansion parameter to investigate the phase structure of scalar
models for the cases of and in 3 dimensions. In particular we
propose a new criterion to distinguish first from second order transitions via
the volume dependence of response functions for couplings close to but not at
the critical value. The criterion is applicable to Monte Carlo simulations as
well. Here it is used to localize the tricritical line in a
theory. We indicate further applications to the electroweak transition.Comment: 3 pages, 1 figure, Talk presented at LATTICE96(Theoretical
Developments
SURFACE INDUCED FINITE-SIZE EFFECTS FOR FIRST ORDER PHASE TRANSITIONS
We consider classical lattice models describing first-order phase
transitions, and study the finite-size scaling of the magnetization and
susceptibility. In order to model the effects of an actual surface in systems
like small magnetic clusters, we consider models with free boundary conditions.
For a field driven transition with two coexisting phases at the infinite volume
transition point , we prove that the low temperature finite volume
magnetization m_{\free}(L,h) per site in a cubic volume of size behaves
like
m_\free(L,h)=\frac{m_++m_-}2 + \frac{m_+-m_-}2
\tanh \bigl(\frac{m_+-m_-}2\,L^d\, (h-h_\chi(L))\bigr)+O(1/L),
where is the position of the maximum of the (finite volume)
susceptibility and are the infinite volume magnetizations at
and , respectively. We show that is shifted by an amount
proportional to with respect to the infinite volume transitions point
provided the surface free energies of the two phases at the transition
point are different. This should be compared with the shift for periodic boun\-
dary conditons, which for an asymmetric transition with two coexisting phases
is proportional only to . One also consider the position of
the maximum of the so called Binder cummulant U_\free(L,h). While it is again
shifted by an amount proportional to with respect to the infinite volume
transition point , its shift with respect to is of the much
smaller order . We give explicit formulas for the proportionality
factors, and show that, in the leading term, the relative shift is
the same as that for periodic boundary conditions.Comment: 65 pages, amstex, 1 PostScript figur
Finite-Size Scaling at Phase Coexistence
{}From a finite-size scaling (FSS) theory of cumulants of the order parameter
at phase coexistence points, we reconstruct the scaling of the moments.
Assuming that the cumulants allow a reconstruction of the free energy density
no better than as an asymptotic expansion, we find that FSS for moments of low
order is still complete. We suggest ways of using this theory for the analysis
of numerical simulations. We test these methods numerically through the scaling
of cumulants and moments of the magnetization in the low-temperature phase of
the two-dimensional Ising model. (LaTeX file; ps figures included as shar file)Comment: preprint HLRZ 27/93 and LU TP 93-
Monte Carlo Study of 8-State Potts Model on 2D Random Lattices
We study the effect of quenched coordination-number disorder of random
lattices on the nature of the phase transition in the two-dimensional
eight-state Potts model, which is of first order on regular lattices. We
consider Poissonian random lattices of toroidal topology constructed according
to the Voronoi/Delaunay prescription. Monte Carlo simulations yield strong
evidence that the phase transition remains first order.Comment: 4 pages, PostScript, contribution to LATTICE95. See also
http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm
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