Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn the finite-size behavior of systems with asymptotically large critical shift
57
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/ u$, with $ u$ being the critical exponent of the bulk correlation length.
rate research
Read More
We present a unified view of finite-size scaling (FSS) in dimension d above the upper critical dimension, for both free and periodic boundary conditions. We find that the modified FSS proposed some time ago to allow for violation of hyperscaling due to a dangerous irrelevant variable, applies only to k=0 fluctuations, and so there is only a single exponent eta describing power-law decay of correlations at criticality, in contrast to recent claims. With free boundary conditions the finite-size shift is greater than the rounding. Nonetheless, using T-T_L, where T_L is the finite-size pseudocritical temperature, rather than T-T_c, as the scaling variable, the data does collapse on to a scaling form which includes the behavior both at T_L, where the susceptibility chi diverges like L^{d/2} and at the bulk T_c where it diverges like L^2. These claims are supported by large-scale simulations on the 5-dimensional Ising model.
We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically-divergent heat capacity. The link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former, and corroborate its predicted scaling form, in the case of the 3d Ising universality class. We show that the scaling behavior emerges clearly when one accounts for the effects of the negative background constant contribution to the canonical critical specific heat. We show that this same constant plays a significant role in determining the observed differences between the canonical and microcanonical specific heats of systems of finite size, in the critical region.
We study critical point finite-size effects in the case of the susceptibility of a film in which interactions are characterized by a van der Waals-type power law tail. The geometry is appropriate to a slab-like system with two bounding surfaces. Boundary conditions are consistent with surfaces that both prefer the same phase in the low temperature, or broken symmetry, state. We take into account both interactions within the system and interactions between the constituents of the system and the material surrounding it. Specific predictions are made with respect to the behavior of a $^3$He and $^4$He films in the vicinity of their respective liquid-vapor critical points.
We study the phase diagram and critical properties of quantum Ising chains with long-range ferromagnetic interactions decaying in a power-law fashion with exponent $alpha$, in regimes of direct interest for current trapped ion experiments. Using large-scale path integral Monte Carlo simulations, we investigate both the ground-state and the nonzero-temperature regimes. We identify the phase boundary of the ferromagnetic phase and obtain accurate estimates for the ferromagnetic-paramagnetic transition temperatures. We further determine the critical exponents of the respective transitions. Our results are in agreement with existing predictions for interaction exponents $alpha > 1$ up to small deviations in some critical exponents. We also address the elusive regime $alpha < 1$, where we find that the universality class of both the ground-state and nonzero-temperature transition is consistent with the mean-field limit at $alpha = 0$. Our work not only contributes to the understanding of the equilibrium properties of long-range interacting quantum Ising models, but can also be important for addressing fundamental dynamical aspects, such as issues concerning the open question of thermalization in such models.
We study critical point finite-size effects on the behavior of susceptibility of a film placed in the Earths gravitational field. The fluid-fluid and substrate-fluid interactions are characterized by van der Waals-type power law tails, and the boundary conditions are consistent with bounding surfaces that strongly prefer the liquid phase of the system. Specific predictions are made with respect to the behavior of $^3$He and $^4$He films in the vicinity of their respective liquid-gas critical points. We find that for all film thicknesses of current experimental interest the combination of van der Waals interactions and gravity leads to substantial deviations from the behavior predicted by models in which all interatomic forces are very short ranged and gravity is absent. In the case of a completely short-ranged system exact mean-field analytical expressions are derived, within the continuum approach, for the behavior of both the local and the total susceptibilities.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
