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1.
Finite size scaling analysis of ising model block distribution functions   总被引:4,自引:0,他引:4  
The distribution functionP L (s) of the local order parameters in finite blocks of linear dimensionL is studied for Ising lattices of dimensionalityd=2, 3 and 4. Apart from the case where the block is a subsystem of an infinite lattice, also the distribution in finite systems with free [P L (f) (s)] and periodic [P L (p)(s) ] boundary conditions is treated. Above the critical pointT c , these distributions tend for largeL towards the same gaussian distribution centered around zero block magnetization, while belowT c these distributions tend towards two gaussians centered at ±M, whereM is the spontaneous magnetization appearing in the infinite systems. However, belowT c the wings of the distribution at small |s| are distinctly nongaussian, reflecting two-phase coexistence. Hence the distribution functions can be used to obtain the interface tension between ordered phases.At criticality, the distribution functions tend for largeL towards scaled universal forms, though dependent on the boundary conditions. These scaling functions are estimated from Monte Carlo simulations. For subsystem-blocks, good agreement with previous renormalization group work of Bruce is obtained.As an application, it is shown that Monte Carlo studies of critical phenomena can be improved in several ways using these distribution functions:(i) standard estimates of order parameter, susceptibility, interface tension are improved(ii) T c can be estimated independent of critical exponent estimates(iii) A Monte Carlo renormalization group similar to Nightingale's phenomenological renormalization is proposed, which yields fairly accurate exponent estimates with rather moderate effort(iv) Information on coarse-grained hamiltonians can be gained, which is particularly interesting if the method is extended to more general Hamiltonians.  相似文献
2.
The analogue of the Edwards-Anderson model for isotropic vector spin glasses, but taking three-component quadrupoles instead of spins at each lattice site, is studied on the square lattice with extensive Monte Carlo calculations, using a nearest-neighbor symmetric gaussian interaction.It is shown that at low temperaturesT the model develops a short range order both with respect to glass like correlations and with respect to ferromagnetic correlations among the quadrupoles. The associated correlation lengths and susceptibilities diverge asT0, and the critical exponents for this zero-temperature phase transition are estimated.Dynamic correlation functions are analyzed as well and it is shown that the dacay of spatially displaced correlations displays a Kohlrausch-Williams-Watts behavior similar to the self-correlation function of the quadrupole moments.Some quantities are compared to their corresponding counterparts on the threedimensional simple cubic lattice, which also has a zero-temperature transition but at corresponding temperatures has stronger short-range-order.  相似文献
3.
    
Critical phenomena in adsorbed monolayers on surfaces are influenced by limited substrate homogeneity, such as surface steps. We consider the resulting finite-size and boundary effects in the framework of a lattice gas system with nearest neighbor attraction in aL×M geometry, with two free boundaries of lengthML, and periodic boundary conditions in the other direction (along the direction of the steps). This geometry thus models a terrace of the stepped surface, and adatoms adsorbed on neighboring terraces are assumed to be non-interacting. Also the effect of boundary fields is considered (describing the effects of missing neighbors and changed binding energy to the substrate near the boundary). Extensive Monte Carlo calculations on this model performed on a multi-transputer system are presented and analyzed in terms of phenomenological finite size scaling concepts. The fact that two scaling variables occur (/L,L/M, with being the correlation length in the bulk) is demonstrated explicitly. In the absence of boundary fields, the system forML orders nearT c in a domain state, with domain walls running across the terrace, while at some temperature belowT c a transition to a monodomain state occurs. This domain state slightly belowT c is suppressed, however, by rather weak boundary fields. These results are interpreted in terms of exact theoretical predictions.  相似文献
4.
Magnetic properties of the Heisenberg antiferromagnet with spin quantum numberS on the face-centered cubic lattice are studied as function of temperature and magnetic field, using molecular field approximation and Monte Carlo methods. In order to model Europiumtelluride, we use isotropic exchange interactions between nearest- and nextnearest neighbors; the values of these exchange constants are taken from experiments. In addition, a pseudo-dipolar anisotropy (truncated after the next-nearest neighbor distance) is included; the molecular field calculations also are performed with the full dipolar of real EuTe in two respects: the structure in zero magnetic field involves 8 sublattices in the model rather than only two; the bicritical point, above which in the temperatureT magnetic fieldH plane the spin flop phase appears, occurs atH=0 in the model rather than at nonzero field. Possible additional interactions responsible for these discrepancies are discussed. Applying finite size scaling techniques we give also a preliminary analysis of the critical behavior of the model.  相似文献
5.
The dynamic behavior at wetting transitions is studied for systems with short-range forces and nonconserved order parameter. From a continuum limit of a purely relaxational lattice model in mean-field approximation, a time-dependent Ginzburg-Landau equation with a time-dependent boundary condition at the surface is derived in the long wavelength approximation. The dynamics of relaxation close to stable and metastable states is treated in linear response. A divergence of the relaxation time occurs both for critical wetting and along the surface spinodal lines (in the case of first-order wetting), although the static surface layer susceptibilities 1, 11 stay finite at the surface spinodal in the non-wet region of the phase diagram.Also the highly nonlinear relaxation that occurs when a wetting layer forms out of an initially non-wet state is considered. For late times, the thickness of the wetting layer grows proportional to the logarithm of time. A comparison with recent Monte Carlo work shows that the present mean-field theory underestimates the prefactor in this growth law. For early times and states in the metastable region a distance H 1 away from the first order wetting transition, the formation of the wet layer starts by heterogeneous nucleation of droplets at the surface. The droplets have the shape of (approximately) caps of a sphere and involve a free energy barrier proportional to (H 1)–2 as H 10. The generalization of this phenomenological approach for the nucleation barrier to the case of long range forces is also discussed and open problems are briefly outlined.  相似文献
6.
The analogue of the Edwards-Anderson model for isotropic vector spin glasses, but taking quadrupoles instead of unit vectors at each lattice site of the considered simple cubic lattice, is studied as a model for an orientational glass. We study both the case where the quadrupole moment can orient in a three-dimensional space (m=3) and the case where the orientation is restricted to a plane (m=2), but otherwise the Hamiltonian is fully isotropic.= , whereJ ij is a random gaussian interaction between nearest neighbors, andS i the 'th component of them-component unit vectorS i at lattice sitei. We define the analogue of the nonlinear susceptibility in spin glasses for the present model and show that it diverges as the temperature is lowered (both casesm=2, andm=3 being consistent with a zero-temperature transition, while form=2 a transition at a nonzero but low temperature cannot be excluded), due to the build-up of long range spatial squared quadrupolar correlations. The time-autocorrelation functionq(t) of the quadrupole moments is analyzed in detail and shown to be consistent with the Kohlrausch law,q(t) exp [–(t/) y ], where the relaxation time diverges asT0, while the exponenty vanishes in this limit.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday  相似文献
7.
Instead of the standard assumption in the theory of phase separation where an instantaneous quench from an initial equilibrium state to the final state in the two-phase region is assumed, we consider the more realistic situation that the change of the external control parameter (e.g. temperature) can only be performed with finite rates. During the initial stages of spinodal decomposition the system then has some memory of the states intermediate between the initial and the final one. This influence of the finite quench rate in continuous quenching procedures is studied within the linearized theory of spinodal decomposition, with the Langer-Baron-Miller decoupling, and with Monte Carlo simulations. Both the case of thermally activated mobilities (applicable to solid metallic alloys) and the case of nearly temperature-independent mobilities (applicable to fluid polymer mixtures) are treated, and possible experimental applications are discussed. We find drastic deviations from the standard instantaneous quench situations in all cases of experimental interest.  相似文献
8.
The fluctuations occurring when an initially disordered system is quenched at timet=0 to a state, where in equilibrium it is ordered, are studied with a scaling theory. Both the mean-sizel(t) d of thed-dimensional ordered domains and their fluctuations in size are found to increase with the same power of the time; their relative size fluctuations are independent of the total volumeL d of the system. This lack of self-averaging is tested for both the Ising model and the 4 model on the square lattice. Both models exhibit the same lawl(t)=(Rt) x withx=1/2, although the 4 model has soft walls. However, spurious results withx1/2 are obtained if bad pseudorandom numbers are used, and if the numbern of independent runs is too small (n itself should be of the order of 103). We also predict a critical singularity of the rateR(1–T/T c) v(z–1/x),v being the correlation length exponent,z the dynamic exponent.Also quenches to the critical temperatureT c itself are considered, and a related lack of self-averaging in equilibrium computer simulations is pointed out for quantities sampled from thermodynamic fluctuation relations.  相似文献
9.
Monte Carlo calculations of the thermodynamic properties (energy, specific heat, magnetization suceptibility, renormalized coupling) of the nearest-neighbour Ising ferromagnet on a five-dimensional hypercubic lattice are presented and analyzed. Lattices of linear dimensionsL=3, 4, 5, 6, 7 with periodic boundary conditions are studied, and a finite size scaling analysis is performed, further confirming the recent suggestion thatL does not scale with the correlation length (the temperature variation of which near the critical temperatureT c is |1-T/T c |–1/2), but rather with a thermodynamic lengthl (withl|1-T/T c |–2/d ,d=5 here). The susceptibility (extrapolated to the thermodynamic limit) agrees quantitatively with high temperature series extrapolations of Guttmann. The problem of fluctuation corrections to the leading (Landau-like) critical behaviour is briefly discussed, and evidence given for a specific-heat singularity of the form |1-T/T c |1/2, superimposed on its leading jump.Dedicated to Prof. Dr. H.E. Müser on the occasion of his 60th birthday  相似文献
10.
The Glauber model is studied for symmetric distributions (±J and gaussian) of the nearest-neighbour interactionJ, including a magnetic field. For small clusters of spins (closed rings ofN bonds, withN7) the complex magnetic susceptibility () and the time-dependent remanent magnetizationm(t) are found exactly for given bond configurations {J ij } by diagonalization of the Liouville operator; apart from the ±J model, the average over {J ij } must be done numerically by simple random sampling Monte Carlo. Nevertheless our accuracy is much better than corresponding dynamic Monte Carlo simulations, even if one considers the extrapolation toN.We analyze the results along the lines of corresponding experimental work, studying the frequency-dependence of the peak in (), theT lnt-scaling ofm(t) at low temperaturesT, and the decomposition of () into a spectrum of relaxation times. Many results are strikingly similar to experimental data for systems such as the Holmium-Borate spinglass or the superparamagnet Eu0.05Sr0.95S, for instance. Frequency-dependent critical fieldsH c () in theH-T plane are also identified but do not have the familiar Almeida-Thouless shape, however.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday  相似文献
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