اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدExact solution of the anisotropic special transition in the O(n) model in 2D
133
0
0.0
(
0
)
تأليف
Jerome Dubail
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
The effect of surface exchange anisotropies is known to play a important role in magnetic critical and multicritical behavior at surfaces. We give an exact analysis of this problem in d=2 for the O(n) model by using Coulomb gas, conformal invariance and integrability techniques. We obtain the full set of critical exponents at the anisotropic special transition--where the symmetry on the boundary is broken down to O(n_1)xO(n-n_1)--as a function of n_1. We also obtain the full phase diagram and crossover exponents. Crucial in this analysis is a new solution of the boundary Yang-Baxter equations for loop models. The appearance of the generalization of Schramm-Loewner Evolution SLE_{kappa,rho} is also discussed.
قيم البحث
اقرأ أيضاً
We derive several closed-form expressions for the fidelity susceptibility~(FS) of the anisotropic $XY$ model in the transverse field. The basic idea lies in a partial fraction expansion of the expression so that all the terms are related to a simple
fraction or its derivative. The critical points of the model are reiterated by the FS, demonstrating its validity for characterizing the phase transitions. Moreover, the critical exponents $ u$ associated with the correlation length in both critical regions are successfully extracted by the standard finite-size scaling analysis.
An exact analytical diagonalization is used to solve the two dimensional Extended Hubbard Model for system with finite size. We have considered an Extended Hubbard Model (EHM) including on-site and off-site interactions with interaction energy U and
V respectively, for square lattice containing 4*4 sites at one-eighth filling with periodic boundary conditions, recently treated by Kovacs et al [1]. Taking into account the symmetry properties of this square lattice and using a translation linear operator, we have constructed a r-space basis, only, with 85 state-vectors which describe all possible distributions for four electrons in the 4*4 square lattice. The diagonalization of the 85*85 matrix energy allows us to study the local properties of the above system as function of the on-site and off-site interactions energies, where, we have shown that the off-site interaction encourages the existence of the double occupancies at the first exited state and induces supplementary conductivity of the system.
We study synchronization in the two-dimensional lattice of coupled phase oscillators with random intrinsic frequencies. When the coupling $K$ is larger than a threshold $K_E$, there is a macroscopic cluster of frequency-synchronized oscillators. We e
xplain why the macroscopic cluster disappears at $K_E$. We view the system in terms of vortices, since cluster boundaries are delineated by the motion of these topological defects. In the entrained phase ($K>K_E$), vortices move in fixed paths around clusters, while in the unentrained phase ($K<K_E$), vortices sometimes wander off. These deviant vortices are responsible for the disappearance of the macroscopic cluster. The regularity of vortex motion is determined by whether clusters behave as single effective oscillators. The unentrained phase is also characterized by time-dependent cluster structure and the presence of chaos. Thus, the entrainment transition is actually an order-chaos transition. We present an analytical argument for the scaling $K_Esim K_L$ for small lattices, where $K_L$ is the threshold for phase-locking. By also deriving the scaling $K_Lsimlog N$, we thus show that $K_Esimlog N$ for small $N$, in agreement with numerics. In addition, we show how to use the linearized model to predict where vortices are generated.
Through a series of exact mappings we reinterpret the Bernoulli model of sequence alignment in terms of the discrete-time totally asymmetric exclusion process with backward sequential update and step function initial condition. Using earlier results
from the Bethe ansatz we obtain analytically the exact distribution of the length of the longest common subsequence of two sequences of finite lengths $X,Y$. Asymptotic analysis adapted from random matrix theory allows us to derive the thermodynamic limit directly from the finite-size result.
Using large-scale numerical simulations we studied the kinetics of the 2d q-Potts model for q > 4 after a shallow subcritical quench from a high-temperature homogeneous configuration. This protocol drives the system across a first-order phase transit
ion. The initial state is metastable after the quench and, for final temperatures close to the critical one, the system escapes from it via a multi-nucleation process. The ensuing relaxation towards equilibrium proceeds through coarsening with competition between the equivalent ground states. This process has been analyzed for different choices of the parameters such as the number of states and the final quench temperature.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
