Narrow Results

The transfer matrix method to describe finite size effects due to tunneling are worked out for Z(2)- and Z(3)-symmetric models. We used this method to extract the surface tension σ in the SU(3) gauge theory at the finite temperature phase transition on lattices with an extent T=2 in the euclidean time direction. We also discuss if the confined phase completely wets the deconfined phase at this first order phase transition.

This brief review discusses methods to locate and characterize first order phase transitions, paying particular attention to finite size effects. In the first part, the order parameter probability distribution and its fourth-order cumulant is discussed for thermally driven first-order transitions (the 3-state Potts model in d=3 dimensions is treated as an example). First-order transitions are characterized by a minimum of the cumulant, which gets very deep for large enough systems. In the second part, we discuss how to locate first order phase boundaries ending in a critical point in a large parameter space. As an example, the study of the unmixing transition of asymmetric polymer mixtures by a combination of histogram techniques and finite size scaling is described.

As a final problem, we discuss the shift of the gas-liquid condensation in thin-film geometry confined between two parallel plates due to boundary fields (“capillary condensation”). Being interested in temperatures far below bulk criticality (e. g. near the wetting transition), special thermodynamic integration techniques are the method of choice, rather than the use of finite sizes scaling to map out the (asymmetric) phase diagram.

Dissipative Particle Dynamics (DPD) simulations were performed to investigate resolution or "coarse graining" effects on the simulation results. Fluid flow through a periodic array of spheres has been studied as a model for fluid filtration into a porous medium. In our model system, it appears that quantitatively correct results for the dimensionless drag can be obtained for relatively small system sizes. For higher solid volume fractions, it is necessary to increase the system size to avoid finite size and resolution effects. Simulations of colloidal spheres suspended in a DPD fluid show effective attraction between the large colloid particles, causing depletion aggregation. This effect may be expected as a consequence of the coarse-grained nature of the DPD fluid. By imposing a steady shear rate the aggregation can be suppressed. The results show that for dilute suspensions, the Brownian noise in the particle interactions causes an effective colloid polydispersity, which suppresses aggregation effects.

The stability of color-flavor locked (CFL) strangelets is studied in the three-flavor Nambu–Jona-Lasinio model. We consider all quark flavors to be massless, for simplicity. By making use of the multiple reflection expansion, we explicitly take into account finite size effects and formulate the thermodynamic potential for CFL strangelets. We find that the CFL gap could be large enough so that the energy per baryon number of CFL strangelets is greatly affected. In addition, if the quark–quark coupling constant is larger than a certain critical value, there is a possibility of finding absolutely stable CFL strangelets.

The properties of two-flavored massless Nambu–Jona-Lasinio (NJL) model in (1+1)-dimensional R¹ × S¹ space–time with compactified space coordinate are investigated in the presence of isospin and quark number chemical potentials μ_I, μ. The consideration is performed in the large N_c limit, where N_c is the number of colored quarks. It is shown that at L = ∞ (L is the length of the circumference S¹) the charged pion condensation (PC) phase with zero quark number density is realized at arbitrary nonzero μ_I and for rather small values of μ. However, at arbitrary finite values of L the phase portrait of the model contains the charged PC phase with nonzero quark number density (in the case of periodic boundary conditions for quark fields). Hence, finite sizes of the system can serve as a factor promoting the appearance of the charged PC phase in quark matter with nonzero baryon densities. In contrast, the phase with chiral symmetry breaking may exist only at rather large values of L.

We have extracted the critical parameters of infinite uncharged nuclear matter from experimental nuclear fragmentation data. To do this, three obstacles had to be overcome: finite size effects, the Coulomb interaction, and an appropriate physical picture (not particles contained in a box) that reflects particle emission into a vacuum.

We consider the Bose-Einstein condensation (BEC) in a relativistic pion gas. The thermodynamic limit when the system volume V goes to infinity as well as the role of finite size effects are studied. At V → ∞ the scaled variance for particle number fluctuations, ω = 〈ΔN²〉/〈N〉, converges to finite values in the normal phase above the BEC temperature, T > T_C. It diverges as ω ∝ V^1/3 at the BEC line T = T_C, and ω ∝ V at T < T_C in a phase with the BE condensate. At high collision energy, in the samples of events with a fixed number of all pions, N, one may observe a prominent signal. When N increases the scaled variances for particle number fluctuations of both neutral and charged pions increase dramatically in the vicinity of the Bose-Einstein condensation line. As an example, the estimates are presented for p + p collisions at the beam energy of 70 GeV.