اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدGeometrical aspect of susceptibility critical exponent
57
0
0.0
(
0
)
تأليف
Q. H. Liu
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Critical exponent $gamma succeq 1.1$ characterizes behavior of the mechanical susceptibility of a real fluid when temperature approaches the critical one. It definitely results in the zero Gaussian curvature of the local shape of the critical point on the thermodynamic equation of state surface, which imposes a new constraint upon the construction of the potential equation of state of the real fluid from the empirical data. All known empirical equations of state suffer from a weakness that the Gaussian curvature of the critical point is negative definite instead of zero, and a new equations of state for the vapor-liquid phase transition with $gamma succ 1$ is constructed.
قيم البحث
اقرأ أيضاً
We uncover an aspect of the Kibble--Zurek phenomenology, according to which the spectrum of critical exponents of a classical or quantum phase transition is revealed, by driving the system slowly in directions parallel to the phase boundary. This res
ult is obtained in a renormalization group formulation of the Kibble--Zurek scenario, and based on a connection between the breaking of adiabaticity and the exiting of the critical domain via new relevant directions induced by the slow drive. The mechanism does not require fine tuning, in the sense that scaling originating from irrelevant operators is observable in an extensive regime of drive parameters. Therefore, it should be observable in quantum simulators or dynamically tunable condensed-matter platforms.
We present a complementary estimation of the critical exponent $alpha$ of the specific heat of the 5D random-field Ising model from zero-temperature numerical simulations. Our result $alpha = 0.12(2)$ is consistent with the estimation coming from the
modified hyperscaling relation and provides additional evidence in favor of the recently proposed restoration of dimensional reduction in the random-field Ising model at $D = 5$.
We present a systematic method to calculate the universal scaling functions for the critical Casimir force and the according potential of the two-dimensional Ising model with various boundary conditions. Therefore we start with the dimer representati
on of the corresponding partition function $Z$ on an $Ltimes M$ square lattice, wrapped around a torus with aspect ratio $rho=L/M$. By assuming periodic boundary conditions and translational invariance in at least one direction, we systematically reduce the problem to a $2times2$ transfer matrix representation. For the torus we first reproduce the results by Kaufman and then give a detailed calculation of the scaling functions. Afterwards we present the calculation for the cylinder with open boundary conditions. All scaling functions are given in form of combinations of infinite products and integrals. Our results reproduce the known scaling functions in the limit of thin films $rhoto 0$. Additionally, for the cylinder at criticality our results confirm the predictions from conformal field theory.
The cosmological redshift phenomenon can be described by the dark matter field fluid model, the results deduced from this model agree very well with the observations. The observed cosmological redshift of light depends on both the speed of the emitte
r and the distance between the emitter and the observer. If the emitter moves away from us, a redshift is observed. If the emitter moves towards us, whether a redshift, a blueshift or no shift is observed will depend on the speed vs. the distance. If the speed is in the range of c(exp[-beta*D]-1) < v < 0, a redshift is observed; if the speed equals c(exp[-beta*D]-1), no shift is observed; if the speed v less than c(exp[-beta*D]-1), a blueshift is observed. A redshift will be always observed in all directions for any celestial objects as long as their distance from us is large enough. Therefore, many more redshifts than blueshifts should be observed for galaxies and supernovae, etc in the sky. This conclusion agrees with current observations. The estimated value of the redshift constant beta of the dark matter field fluid is in the range of 10^(-3) ~ 10^(-5)/Mpc. A large redshift value from a distant celestial object may not necessarily indicate that it has a large receding speed. Based on the redshift effect of dark matter field fluid, it is concluded that at least in time average all photons have the same geometry (size and shape) in all inertial reference frames and do not have length contraction effect.
We study the critical behavior of the Ising model in three dimensions on a lattice with site disorder by using Monte Carlo simulations. The disorder is either uncorrelated or long-range correlated with correlation function that decays according to a
power-law $r^{-a}$. We derive the critical exponent of the correlation length $ u$ and the confluent correction exponent $omega$ in dependence of $a$ by combining different concentrations of defects $0.05 leq p_d leq 0.4$ into one global fit ansatz and applying finite-size scaling techniques. We simulate and study a wide range of different correlation exponents $1.5 leq a leq 3.5$ as well as the uncorrelated case $a = infty$ and are able to provide a global picture not yet known from previous works. Additionally, we perform a dedicated analysis of our long-range correlated disorder ensembles and provide estimates for the critical temperatures of the system in dependence of the correlation exponent $a$ and the concentrations of defects $p_d$. We compare our results to known results from other works and to the conjecture of Weinrib and Halperin: $ u = 2/a$ and discuss the occurring deviations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
