Quantitative Theory of Critical Phenomena
Quantitative Theory of Critical Phenomena details in a self-contained manner the most popular and extensively practiced methods for the quantitative study of critical phenomena.
The text is divided into three parts. Part I deals with the general theory of critical phenomena — its thermodynamic aspects, statistical mechanical framework, classical model, and inequalities. Part II tackles the combinatorial theory of series generation. Part III covers the quantitative analysis of series expansions, which includes topics such as the complex variable theory, the algebraic aspects and numerical evaluation of Padé approximants, and special continuation methods.
The book is recommended for mathematicians and physicists who would like to know more about critical phenomena, its theories, and the methods for its quantitative study.
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algebra analytic continuation analytic function asymptotic Baker behavior bond branch point Chapter coefﬁcients complex plane compute conﬁgurations connected graphs correlation function corresponding critical exponents critical indices critical phenomena critical point deﬁne deﬁnition denote derivative diagonal disk edges eigenvalues equations example exists expansion factor ferromagnetic ﬁeld theory ﬁnd ﬁnite number ﬁrst ﬁxed point follows formula functional element Gaussian model given gives Grifﬁths identity illustrated implies inequality inﬁnite integral approximants integral polynomials invariance Ising model labelled limit linear linearly independent magnetic ﬁeld matrix mean ﬁeld method monodromy notation Padé approximants Padé table partition function poles problem proof radius of convergence reﬂection region renormalization group satisﬁes sequence series of Stieltjes singular points solution speciﬁc heat spin spin-spin correlation Taylor series temperature thermodynamic potentials transformation unique values variable vector vertex vertices zero