254 research outputs found
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
First-order transition features of the triangular Ising model with nearest- and next-nearest-neighbor antiferromagnetic interactions
We implement a new and accurate numerical entropic scheme to investigate the
first-order transition features of the triangular Ising model with
nearest-neighbor () and next-nearest-neighbor ()
antiferromagnetic interactions in ratio . Important aspects
of the existing theories of first-order transitions are briefly reviewed,
tested on this model, and compared with previous work on the Potts model. Using
lattices with linear sizes and 480 we
estimate the thermal characteristics of the present weak first-order
transition. Our results improve the original estimates of Rastelli et al. and
verify all the generally accepted predictions of the finite-size scaling theory
of first-order transitions, including transition point shifts, thermal, and
magnetic anomalies. However, two of our findings are not compatible with
current phenomenological expectations. The behavior of transition points,
derived from the number-of-phases parameter, is not in accordance with the
theoretically conjectured exponentially small shift behavior and the well-known
double Gaussian approximation does not correctly describe higher correction
terms of the energy cumulants. It is argued that this discrepancy has its
origin in the commonly neglected contributions from domain wall corrections.Comment: 34 pages, 11 figure
Longitudinal spin relaxation in simple stochastic models for disordered systems
The relaxation of single probe spins was investigated for simple models of systems with quenched disorder. The spin relaxation was calculated for a two-site model with arbitrarily oriented magnetic fields and the result was averaged over various distributions of the fields, and of the hopping rates of the spin. On an intermediate time scale, a modified Kubo-Toyabe behavior is obtained for large hopping rates, in agreement with recent SR experiments. A stretched-exponential decay of the spin polarization is obtained at longer times. The Kohlrausch exponent is found to be field and hopping-rate dependent, in qualitative agreement with recent NMR and -NMR experiments. The resulting longitudinal relaxation rate still does not show the significant deviations from the Bloembergen-Purcell-Pound (BPP) behavior that are typical for glassy systems. Therefore, the random two-frequency model was extended to include time-dependent renewals of the environment. This modification may yield asymmetric peaks for the longitudinal relaxation rate in the BPP plot for very large renewal rates. © 1995 The American Physical Society
Finite Size Effects in Fluid Interfaces
It is shown that finite size effects in the free energy of a rough interface
of the 3D Ising and three--state Potts models are well described by the
capillary wave model at {\em two--loop} order. The agreement between
theoretical predictions and Monte Carlo simulations strongly supports the idea
of the universality of this description of order--order interfaces in 3D
statistical systems above the roughening temperature.Comment: 3 pages, uuencoded .ps file, figures included. (Proceeding of Lattice
'93
Fisher Zeroes and Singular Behaviour of the Two Dimensional Potts Model in the Thermodynamic Limit
The duality transformation is applied to the Fisher zeroes near the
ferromagnetic critical point in the q>4 state two dimensional Potts model. A
requirement that the locus of the duals of the zeroes be identical to the dual
of the locus of zeroes in the thermodynamic limit (i) recovers the ratio of
specific heat to internal energy discontinuity at criticality and the
relationships between the discontinuities of higher cumulants and (ii)
identifies duality with complex conjugation. Conjecturing that all zeroes
governing ferromagnetic singular behaviour satisfy the latter requirement gives
the full locus of such Fisher zeroes to be a circle. This locus, together with
the density of zeroes is then shown to be sufficient to recover the singular
form of the thermodynamic functions in the thermodynamic limit.Comment: 10 pages, 0 figures, LaTeX. Paper expanded and 2 references added
clarifying duality relationships between discontinuities in higher cumulant
Simulation of fatigue-initiated subacromial impingement: clarifying mechanisms
AbstractSubacromial impingement in the shoulder precedes many cases of rotator cuff pathology. However, debate exists regarding the mechanism, and even existence, of fatigue-initiated impingement. The controversy centers on two primary impingement mechanisms: 1) superior humeral head migration and 2) scapular reorientation. A linked series of in vivo experiments and in silica simulations accomplishes the integration of stochastic, orthopedic, geometric, kinematic, physiologic, literature-derived, and experimental data sources to help resolve the mechanism debate. A major focus is the multi-scale modeling of relevant variability. The described techniques have direct implications for musculoskeletal modeling and simulation of the shoulder region, with specific application to assessing occupational and activities of daily living in diverse populations
Multigraph limit of the dense configuration model and the preferential attachment graph
The configuration model is the most natural model to generate a random
multigraph with a given degree sequence.
We use the notion of dense graph limits to characterize the special form of
limit objects of convergent sequences of configuration models. We apply these
results to calculate the limit object corresponding to the dense preferential
attachment graph and the edge reconnecting model. Our main tools in doing so
are (1) the relation between the theory of graph limits and that of partially
exchangeable random arrays (2) an explicit construction of our random graphs
that uses urn models.Comment: Some of the results of this submission already appeared in an older
version of arXiv:0912.3904v3, "Time evolution of dense multigraph limits
under edge-conservative preferential attachment dynamics." Accepted for
publication in Acta Mathematica Hungaric
Monte Carlo Study of Cluster-Diameter Distribution: A New Observable to Estimate Correlation Lengths
We report numerical simulations of two-dimensional -state Potts models
with emphasis on a new quantity for the computation of spatial correlation
lengths. This quantity is the cluster-diameter distribution function
, which measures the distribution of the diameter of
stochastically defined cluster. Theoretically it is predicted to fall off
exponentially for large diameter , , where
is the correlation length as usually defined through the large-distance
behavior of two-point correlation functions. The results of our extensive Monte
Carlo study in the disordered phase of the models with , 15, and on
large square lattices of size , , and , respectively, clearly confirm the theoretically predicted behavior.
Moreover, using this observable we are able to verify an exact formula for the
correlation length in the disordered phase at the first-order
transition point with an accuracy of about for all considered
values of . This is a considerable improvement over estimates derived from
the large-distance behavior of standard (projected) two-point correlation
functions, which are also discussed for comparison.Comment: 20 pages, LaTeX + 13 postscript figures. See also
http://www.cond-mat.physik.uni-mainz.de/~janke/doc/home_janke.htm
The free energy of the Potts model: from the continuous to the first-order transition region
We present a large expansion of the 2d -states Potts model free
energies up to order 9 in . Its analysis leads us to an ansatz
which, in the first-order region, incorporates properties inferred from the
known critical regime at , and predicts, for , the
energy cumulant scales as the power of the correlation length. The
parameter-free energy distributions reproduce accurately, without reference to
any interface effect, the numerical data obtained in a simulation for
with lattices of linear dimensions up to L=50. The pure phase specific heats
are predicted to be much larger, at , than the values extracted from
current finite size scaling analysis of extrema. Implications for safe
numerical determinations of interface tensions are discussed.Comment: 11 pages, plain tex with 3 Postscript figures included Postscript
file available by anonymous ftp://amoco.saclay.cea.fr/pubs.spht/93-022.p
Glassiness Vs. Order in Densely Frustrated Josephson Arrays
We carry out extensive Monte Carlo simulations on the Coulomb gas dual to the
uniformly frustrated two dimensional XY model, for a sequence of frustrations f
converging to the irraltional (3-sqrt 5)/2. We find in these systems a sharp
first order equilibrium phase transition to an ordered vortex structure at a
T_c which varies only slightly with f. This ordered vortex structure remains in
general phase incoherent until a lower pinning transition T_p(f) that varies
with f. We argue that the glassy behaviors reported for this model in earlier
simulations are dynamic effects.Comment: 4 pages, 4 eps figure
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