We note that the standard inverse system volume scaling for finite-size corrections at a firstorder phase transition (i.e., 1/L 3 for an L × L × L lattice in 3D) is transmuted to 1/L 2 scaling if there is an exponential low-temperature phase degeneracy. The gonihedric Ising model which has a four-spin interaction, plaquette Hamiltonian provides an exemplar of just such a system. We use multicanonical simulations of this model to generate high-precision data which provides strong confirmation of the non-standard finite-size scaling law. The dual to the gonihedric model, which is an anisotropically coupled Ashkin-Teller model, has a similar degeneracy and also displays the non-standard scaling.PACS numbers: 05.50.+q, 05.70.Jk, 75.10.Hk First-order phase transitions are ubiquitous in nature [1]. Pioneering studies of finite-size scaling for first-order transitions were carried out in [2] and subsequently pursued in detail in [3]. Rigorous results for periodic boundary conditions were further derived in [4,5]. It is possible to go quite a long way in discussing the scaling laws for such first-order transitions using a simple heuristic twophase model [6]. We assume that a system spends a fraction W o of the total time in one of the q ordered phases and a fraction W d = 1 − W o in the disordered phase with corresponding energiesê o andê d , respectively. The hat is introduced for quantities evaluated at the inverse transition temperature of the infinite system, β ∞ . Neglecting all fluctuations within the phases and treating the phase transition as a sharp jump between the phases, the energy moments become e n = W oê, where the disordered and ordered peaks of the energy probability density have equal weight. The probability of being in any of the ordered states or the disordered state is related to the free energy densitiesf o ,f d of the states,and by construction the fraction of time spent in the ordered states must be proportional to qp o . Thus for the ratio of fractions we find (up to exponentially small corrections in L [4-7]). Taking the logarithm of this ratio gives ln(WAt the specific-heat maximum W o = W d , so we find by an expansion around βwhich can be solved for the finite-size peak location of the specific heat:Although this is a rather simple toy model, it is known to capture the essential features of first-order phase transitions and to correctly predict the prefactors of the leading finite-size scaling corrections for a class of models with a contour representation, such as the q-state Potts model, where a rigorous theory also exists [5]. Similar calculations give [6,8] for the location β Normally the degeneracy q of the low-temperature phase does not change with system size and the generic finite-size scaling behaviour of a first-order transition thus has a leading contribution proportional to the inverse volume L −d . We can see from Eqs. (4), (5) that if the degeneracy q of the low-temperature phase depends exponentially on the system size, q ∝ e L , this would be modified. One model with preci...

The three-dimensional purely plaquette gonihedric Ising model and its dual are investigated to resolve inconsistencies in the literature for the values of the inverse transition temperature of the very strong temperature-driven first-order phase transition that is apparent in the system. Multicanonical simulations of this model allow us to measure system configurations that are suppressed by more than 60 orders of magnitude compared to probable states. With the resulting high-precision data, we find excellent agreement with our recently proposed nonstandard finite-size scaling laws for models with a macroscopic degeneracy of the low-temperature phase by challenging the prefactors numerically. We find an overall consistent inverse transition temperature of β ∞ = 0.551334(8) from the simulations of the original model both with periodic and fixed boundary conditions, and the dual model with periodic boundary conditions. For the original model with periodic boundary conditions, we obtain the first reliable estimate of the interface tension σ = 0.12037(18), using the statistics of suppressed configurations.

We investigate the aggregation transition of theta polymers in spherical confinement with multicanonical simulations. This allows for a systematic study of the effect of density on the aggregation transition temperature for up to 24 monodisperse polymers. Our results for solutions in the dilute regime show that polymers can be considered isolated for all temperatures larger than the aggregation temperature, which is shown to be a function of the density. The resulting competition between single-polymer collapse and aggregation yields the lower temperature bound of the isolated chain approximation. We provide entropic and energetic arguments to describe the density dependence and finite-size effects of the aggregation transition for monodisperse solutions in finite systems. This allows us to estimate the aggregation transition temperature of dilute systems in a spherical cavity, using a few simulations of small, sufficiently dilute polymer systems.

Seaweed (SW) is employed as filler to prepare composites on the basis of a polypropylene (PP) matrix in the ratio of 10 : 90, 20 : 80, 30 : 70, 40 : 60, and 50 : 50 (wt % SW : wt % PP) by compounding and injection molding. The tensile, bending and impact properties of the composites were investigated. The 30% SW : 70% PP composite showed the best over-all mechanical performance of the composites prepared. Further improvement of this optimal composite was achieved by incorporating 2% thermoplastic elastomer (TPE) as additive. Interfacial adhesion and bonding between the fibers and PP matrix were investigated by scanning electron microscopy (SEM). Water absorption tests of the different composites were also performed, and addition of TPE was found to lead to a substantial reduction of water uptake.

Abstract. We review some recent investigations of the 3d plaquette Ising model. This displays a strong first-order phase transition with unusual scaling properties due to the size-dependent degeneracy of the low-temperature phase. In particular, the leading scaling correction is modified from the usual inverse volume behaviour ∝ 1/L 3 to 1/L 2 . The degeneracy also has implications for the magnetic order in the model which has an intermediate nature between local and global order and gives rise to novel fracton topological defects in a related quantum Hamiltonian.