Intrinsic finite-size effects in the two-dimensional XY model with irrational frustration

This study investigates in detail the finite-size scaling of the two-dimensional irrationally frustrated XY model. By means of Monte Carlo simulations with entropic sampling, we examine the size dependence of the specific heat, and find remarkable deviation from the conventional finite-size scaling theory, which reveals novel intrinsic finite-size effects. Relaxation dynamics of the system is also considered, and, correspondingly, finite-size scaling of the relaxation time is examined, again giving evidence for the intrinsic finite-size effects and suggesting a zero-temperature glass transition.     

Chiral-glass transition in a diluted dipolar-interaction Heisenberg system

Recently, numerical simulations reveal that a spin-glass transition can occur in the three-dimensional diluted dipolar system. By defining the chirality of triple spins in a diluted dipolar Heisenberg spin glass, we study the chiral ordering in the system using parallel tempering algorithm and heat bath method. The finite-size scaling analysis reveals that the system undergoes a chiral-glass transition at finite temperature.     

Finite-size scaling of the three-state Potts model on a simple cubic lattice

Finite-size scaling is studied for the three-state Potts model on a simple cubic lattice. We show that the specific heat and the magnetic susceptibility scale accurately as the volume. The correlation length exhibits behaviors expected for a genuine first-order transition; the one extracted from the unsubtracted correlation function shows a characteristic finite-size behavior, whereas the physical correlation length that characterizes the first excited state stays at a finite value and is discontinuous at the transition point.     

First-order transitions and thermodynamic properties in the 2D Blume-Capel model: the transfer-matrix method revisited

We investigate the first-order transition in the spin-1 two-dimensional Blume-Capel model in square lattices by revisiting the transfer-matrix method. With large strip widths increased up to the size of 18 sites, we construct the detailed phase coexistence curve which shows excellent quantitative agreement with the recent advanced Monte Carlo results. In the deep first-order area, we observe the exponential system-size scaling of the spectral gap of the transfer matrix from which linearly increasing interfacial tension is deduced with decreasing temperature. We find that the first-order signature at low temperatures is strongly pronounced with much suppressed finite-size influence in the examined thermodynamic properties of entropy, non-zero spin population, and specific heat. It turns out that the jump at the transition becomes increasingly sharp as it goes deep into the first-order area, which is in contrast to the Wang–Landau results where finite-size smoothing gets more severe at lower temperatures.     

Specific heat of helium confined to a 57- &mgr;m planar geometry near the lambda point

We report measurements of the specific heat of liquid helium confined to 57-&mgr;m planar gaps extending to within a few nanokelvin of the bulk lambda transition. The data are in fair agreement with Monte Carlo estimates for finite-size effects and with renormalization-group-theory predictions above the transition. Far from the transition, we find surface specific heat exponents, alpha(s) = 0.64+/-0.05 below, and 0.65+/-0.2 above, which compare well with the prediction of 0.658. Comparison with other recent data on small length scales shows some areas of agreement.     

Counterions at charged cylinders: criticality and universality beyond mean-field theory

The counterion-condensation transition at charged cylinders is studied using Monte Carlo simulations. Employing logarithmically rescaled radial coordinates, large system sizes are tractable and the critical behavior is determined by a combined finite-size and finite-ion-number analysis. Critical counterion localization exponents are introduced and found to be in accord with mean-field theory both in two (2D) and three (3D) dimensions. In 3D, the heat capacity shows a universal jump at the transition, while in 2D, it consists of discrete peaks where single counterions successively condense.     

Three-dimensional critical behavior with 2D, 1D, and 0D dimensionality crossover: surface and edge specific heats

The critical behavior at a second order phase transition is characterized by the divergence of the correlation length xi. We have studied the superfluid transition of 4He in a series of experimental cells in which this divergence of xi is modified due to finite-size confinement. In particular, the design of these cells is such that the smallest dimension is kept the same, 1 microm, but the geometry is such that one obtains crossover to dimensionality of 2, 1, and 0. This corresponds to films, channels, and boxes filled with helium. We measure the specific heat and compare these results with theoretical expectations. We identify surface and line specific heat contributions by analyzing the deviation of the specific heat from its behavior in the thermodynamic limit. The design of these cells is made possible by a combination of silicon lithography and direct wafer bonding.     

有限尺度下弱相互作用费米气体的热力学性质

基于巨正则系综理论和数值模拟方法，研究有限尺度下弱相互作用费米气体的热力学性质，给出系统低温下的化学势、能量及热容量的解析式，分析弱相互作用、有限尺度效应对系统热力学性质的影响.研究表明，有限尺度和排斥相互作用增大了系统的化学势、能量,吸引相互作用减小了系统的化学势、能量.相互作用受到尺度的调制，尺度变大，相互作用影响变小，相互作用和尺度效应都受到温度的调制，温度升高，相互作用和尺度的影响减小.尺度和相互作用的一级修正对热容量无影响.     

有限尺度下弱相互作用费米气体的热力学性质

基于巨正则系综理论和数值模拟方法,研究有限尺度下弱相互作用费米气体的热力学性质,给出系统低温下的化学势、能量及热容量的解析式,分析弱相互作用、有限尺度效应对系统热力学性质的影响.研究表明,有限尺度和排斥相互作用增大了系统的化学势、能量,吸引相互作用减小了系统的化学势、能量.相互作用受到尺度的调制,尺度变大,相互作用影响变小,相互作用和尺度效应都受到温度的调制,温度升高,相互作用和尺度的影响减小.尺度和相互作用的一级修正对热容量无影响.     

Interfacial adsorption phenomena at a weakly first-order phase transition

We study the interfacial adsorption phenomena of the ferromagnetic five-state Potts model on the square lattice, whose transition is of weakly first-order, by using Monte Carlo simulations and finite-size scaling theory. It is shown that the net-adsorption has a finite-size effect according to the first-order phase transition even for systems much smaller than the bulk correlation length.     

Investigation of the critical properties of the three-dimensional weakly diluted potts model

The problem of the type of the phase transition in the three-dimensional weakly diluted Potts model with the number of spin states q= 3 has been investigated by the Monte Carlo method. The temperature dependences of the Binder cumulants, energy, magnetization, specific heat, and susceptibility have been calculated. It is found that the second-order phase transition occurs in a system at the spin concentration p = 0.9. The critical exponents of the magnetization (β), specific heat (α), and susceptibility (γ) and the critical correlation-length exponent v were calculated on the basis of the finite-size scaling theory at p = 0.9.     

Reduction of surface coverage of finite systems due to geometrical steps

The coverage of vicinal, stepped surfaces with molecules is simulated with the help of a two-dimensional Ising model including local distortions and an Ehrlich-Schwoebel barrier term at the steps. An effective two-spin model is capable to describe the main properties of this distorted Ising model. It is employed to analyze the behavior of the system close to the critical points. Within a well-defined regime of bonding strengths and Ehrlich-Schwoebel barriers we find a reduction of coverage (magnetization) at low temperatures due to the presence of the surface step. This results in a second, low-temperature transition besides the standard Ising order-disorder transition. The additional transition is characterized by a divergence of the susceptibility as a finite-size effect. Due to the surface step the mean-field specific heat diverges with a power law.     

Monte Carlo Study of Planar Rotator Model with Weak Dzyaloshinsky-Moriya Interaction

With the help of an improvement Monte Carlo method, the Berezinskii-Kosterlitz-Thouless phase transition arising in two-dimensional planar rotator model with weak Dzyaloshinsky-Moriya (DM) interaction is investigated. The effects of the DM interaction on specific heat, susceptibility, and magnetization are simulated. The critical temperature of transitions is determined by the so-called Binder cumulant and the susceptibility of finite-size scaling. We find that the chiral Z2 symmetry reduced by the DM interactions plays an important role in a two-dimensional XY spin system,typically, the critical temperature is sensitive to weak DM spin couplings.     

Thermodynamic properties of a finite Bose gas in a harmonic trap

We have investigated the thermodynamic behaviour of ideal Bose gases with an arbitrary number of particles confined in a harmonic potential. By taking into account the conservation of total number $N$ of particles and using a saddle-point approximation, we derive analytically the simple explicit expression of mean occupation number in any state of the finite system. The temperature dependence of the chemical potential, specific heat, and condensate fraction for the trapped finite-size Bose system is obtained numerically. We compare our results with the usual treatment which is based on the grand canonical ensemble. It is shown that there exists a considerable difference between them at sufficiently low temperatures, specially for the relative small numbers of Bose atoms. The finite-size scaling at the transition temperature for the harmonically trapped systems is also discussed. We find that the scaled condensate fractions for various system sizes and temperatures collapse onto a single scaled form.     

Anomalous mass dependence of radiative quark energy loss in a finite-size quark-gluon plasma

We demonstrate that for a finite-size quark-gluon plasma the induced gluon radiation from heavy quarks is stronger than that for light quarks when the gluon formation length becomes comparable with (or exceeds) the size of the plasma. The effect is due to oscillations of the light-cone wave function for the in-medium q→gq transition. The dead cone model by Dokshitzer and Kharzeev neglecting quantum finite-size effects is not valid in this regime. The finite-size effects also enhance the photon emission from heavy quarks.     

Phase diagram of the three-dimensional Hubbard model at half filling

We investigate the phase diagram of the three-dimensional Hubbard model at half filling using quantum Monte Carlo (QMC) simulations. The antiferromagnetic Néel temperature is determined from the specific heat maximum in combination with finite-size scaling of the magnetic structure factor. Our results interpolate smoothly between the asymptotic solutions for weak and strong coupling, respectively, in contrast to previous QMC simulations. The location of the metal-insulator transition in the paramagnetic phase above is determined using the electronic compressibility as criterion. Received 11 April 2000 and Revised in final form 29 June 2000     

3D Icosahedral aperiodic packings of spheres of different diameters from discrete icosahedral crystals

General results for transient pattern dynamics in the context of spinodal decomposition as well as domain-wall formation in the Fréedericksz transition in nematics are reviewed. The question of wavelength selection and the relevance of finite-size effects in this issue are considered in a general model of transient pattern dynamics. A finite-size scaling law for domain growth is shown to be satisfied by this model.     

Finite-size scaling analysis of the glass transition

We show that finite-size scaling techniques can be employed to study the glass transition. Our results follow from the postulate of a diverging dynamical correlation length at the glass transition whose physical manifestation is the presence of dynamical heterogeneities. We introduce a parameter B(T,L) whose temperature, T, and system size, L, dependences permit a precise location of the glass transition. We discuss the finite-size scaling behavior of a diverging susceptibility chi(L,T). These new techniques are successfully used to study two lattice models. The analysis straightforwardly applies to any glass-forming system.     

Interface localization-delocalization in a double wedge: a new universality class with strong fluctuations and anisotropic scaling

Using Monte Carlo simulations and finite-size scaling methods we study "wetting" in Ising systems in a LxLxL(y) pore with quadratic cross section. Antisymmetric surface fields H(s) act on the free LxL(y) surfaces of the opposing wedges, and periodic boundary conditions are applied along the y direction. In the limit L--> infinity, L(y)/L(3)=const, the system exhibits a new type of phase transition, which is the analog of the "filling transition" that occurs in a single wedge. It is characterized by critical exponents alpha=3/4, beta=0, and gamma=5/4 for the specific heat, order parameter, and susceptibility, respectively.     

超薄膜磁性材料上XY模型的临界现象

采用经典XY模型，阐明了三角格子上层状超薄膜磁性材料的相变和临界现象.并用Monte-Carlo方法对该模型的内部能量、比热、chirality等热力学量进行了计算.使用finite-size scaling 分析法对临界现象的性质进行了论述.通过上述分析和计算，发现该模型在反强磁性层与强磁性层内的chirality在一定范围内随温度的变化急剧增加，这是一种新的chirality相变；而在另一范围内存在Kosterliz-Thouless相变和通常的chirality相变.这种新的chirality相变的 关键词： 层状XY模型 临界现象 Monte-Carlo模拟 磁性薄膜