Critical Exponents of O(n)-symmetric Theory
نویسندگان
چکیده
We shall now use the results of the previous chapters to derive explicitly the critical exponents of the O(N)-symmetric φ 4-theory. The unique tensor multiplying the product of fields φ α φ β φ γ φ δ in the interaction is [recall (6.25)]
منابع مشابه
Self-similar variational perturbation theory for critical exponents.
We extend field theoretic variational perturbation theory by self-similar approximation theory, which greatly accelerates convergence. This is illustrated by recalculating the critical exponents of O (N) -symmetric phi(4) theory. From only three-loop perturbation expansions in 4-epsilon dimensions, we obtain analytic results for the exponents, which are close to those derived recently from ordi...
متن کاملDerivative expansion of the renormalization group in O(N) scalar field theory
We apply a derivative expansion to the Legendre effective action flow equations of O(N) symmetric scalar field theory, making no other approximation. We calculate the critical exponents η, ν, and ω at the both the leading and second order of the expansion, associated to the three dimensional Wilson-Fisher fixed points, at various values of N . In addition, we show how the derivative expansion r...
متن کامل4 v 1 3 1 M ar 1 99 8 Critical exponents for 3 D O ( n ) – symmetric model with n > 3
Critical exponents for the 3D O(n)–symmetric model with n > 3 are estimated on the base of six–loop renormalisation–group (RG) expansions. Simple Padé–Borel technique is used for resummation of RG series and Padé approximants [L/1] are shown to give rather good numerical results for all calculated quantities. For large n, the fixed point location gc and critical exponents are also determined di...
متن کاملCritical Phenomena and Renormalization-Group Theory
We review results concerning the critical behavior of spin systems at equilibrium. We consider the Ising and the general O(N)-symmetric universality class. For each of them, we review the estimates of the critical exponents, of the equation of state, of several amplitude ratios, and of the two-point function of the order parameter. We report results in three and two dimensions. We discuss the c...
متن کاملCalculation of critical exponents by self-similar factor approximants
The method of self-similar factor approximants is applied to calculating the critical exponents of the O(N)-symmetric φ4 theory and of the Ising glass. It is demonstrated that this method, being much simpler than other known techniques of series summation in calculating the critical exponents, at the same time, yields the results that are in very good agreement with those of other rather compli...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010