اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدStatic replica approach to critical correlations in glassy systems
122
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We discuss the slow relaxation phenomenon in glassy systems by means of replicas by constructing a static field theory approach to the problem. At the mean field level we study how criticality in the four point correlation functions arises because of the presence of soft modes and we derive an effective replica field theory for these critical fluctuations. By using this at the Gaussian level we obtain many physical quantities: the correlation length, the exponent parameter that controls the Mode-Coupling dynamical exponents for the two-point correlation functions, and the prefactor of the critical part of the four point correlation functions. Moreover we perform a one-loop computation in order to identify the region in which the mean field Gaussian approximation is valid. The result is a Ginzburg criterion for the glass transition. We define and compute in this way a proper Ginzburg number. Finally, we present numerical values of all these quantities obtained from the Hypernetted Chain approximation for the replicated liquid theory.
قيم البحث
اقرأ أيضاً
It is shown that the limit $t-ttoinfty$ of the equilibrium dynamic self-energy can be computed from the $nto 1$ limit of the static self-energy of a $n$-times replicated system with one step replica symmetry breaking structure. It is also shown that
the Dyson equation of the replicated system leads in the $nto 1$ limit to the bifurcation equation for the glass ergodicity breaking parameter computed from dynamics. The equivalence of the replica formalism to the long time limit of the equilibrium relaxation dynamics is proved to all orders in perturbation for a scalar theory.
We endow a system of interacting particles with two distinct, local, Markovian and reversible microscopic dynamics. Using common field-theoretic techniques used to investigate the presence of a glass transition, we find that while the first, standard
, dynamical rules lead to glassy behavior, the other one leads to a simple exponential relaxation towards equilibrium. This finding questions the intrinsic link that exists between the underlying, thermodynamical, energy landscape, and the dynamical rules with which this landscape is explored by the system. Our peculiar choice of dynam- ical rules offers the possibility of a direct connection with replica theory, and our findings therefore call for a clarification of the interplay between replica theory and the underlying dynamics of the system.
We present a numerical method for the evaluation of the mass gap, and the low-lying energy gaps, of a large family of free-fermionic and free-parafermionic quantum chains. The method is suitable for some generalizations of the quantum Ising and XY mo
dels with multispin interactions. We illustrate the method by considering the Ising quantum chains with uniform and random coupling constants. The mass gaps of these quantum chains are obtained from the largest root of a characteristic polynomial. We also show that the Laguerre bound, for the largest root of a polynomial, used as an initial guess for the largest root in the method, gives us estimates for the mass gaps sharing the same leading finite-size behavior as the exact results. This opens an interesting possibility of obtaining precise critical properties very efficiently which we explore by studying the critical point and the paramagnetic Griffiths phase of the quantum Ising chain with random couplings. In this last phase, we obtain the effective dynamical critical exponent as a function of the distance-to-criticality. Finally, we compare the mass gap estimates derived from the Laguerre bound and the strong-disorder renormalization-group method. Both estimates require comparable computational efforts, with the former having the advantage of being more accurate and also being applicable away from infinite-randomness fixed points. We believe this method is a new and relevant tool for tackling critical quantum chains with and without quenched disorder.
We consider two models with disorder dominated critical points and study the distribution of clusters which are confined in strips and touch one or both boundaries. For the classical random bond Potts model in the large-q limit we study optimal Fortu
in-Kasteleyn clusters by combinatorial optimization algorithm. For the random transverse-field Ising chain clusters are defined and calculated through the strong disorder renormalization group method. The numerically calculated density profiles close to the boundaries are shown to follow scaling predictions. For the random bond Potts model we have obtained accurate numerical estimates for the critical exponents and demonstrated that the density profiles are well described by conformal formulae.
We present a theoretical discussion of the reversible parking problem, which appears to be one of the simplest systems exhibiting glassy behavior. The existence of slow relaxation, nontrivial fluctuations, and an annealing effect can all be understoo
d by recognizing that two different time scales are present in the problem. One of these scales corresponds to the fast filling of existing voids, the other is associated with collective processes that overcome partial ergodicity breaking. The results of the theory are in a good agreement with simulation data; they provide a simple qualitative picture for understanding recent granular compaction experiments and other glassy systems.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
