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- W197848319 abstract "To understand multicriticality the first step is to understand ordinary critical behavior and, in particular, the theory of scaling. Ferromagnetic criticality provides the simplest example whichsuffices to define the critical exponents α,s,γ, etc.; the concept of universality classes depending on spatial dimensionality, d, and spin dimensionality, n; the basic nature of scaling and consequent exponent relations; the universality of the scaling functions and amplitude ratios. Study of fluid criticality reveals the importance and the significance of scaling axes and the linear scaling fields, say, (tilde t{text{ and }}tilde h), which are combinations of the physical fields t = (T-Tc)/Tc and h = (µ-µc)/kBT 1,2 : the primary scaling axis is obvious from the orientation of the first order phase boundary; the secondary axis is less obvious but its slope leads, for example, to a |t|1-α singularity in the diameter of the coexistence curve . Then it is important to recognize the existence of nonlinear scaling fields, which can be represented by multiplying (tilde t{text{ and }}tilde h) by analytic functions of t and h. These enter even when symmetry dictates the linear scaling axes and they lead, for example, to |t|1-α additive terms in the initial susceptibility of a ferromagnet3. Similarly, in the case of a lambda or critical line, they lead to the prediction that the specific heat singularity of an anti ferromagnet in zero field should match that in ∂(χT)/∂T, where χ is the differential susceptibility4. Finally, renormalization group theory5 leads to singular correction factors of the form ((1 + {c_1}{t^theta } + ...)) with, typically, (theta simeq 1/2 < 1.)." @default.
- W197848319 created "2016-06-24" @default.
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- W197848319 date "1984-01-01" @default.
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- W197848319 title "Multicriticality: A Theoretical Introduction" @default.
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- W197848319 doi "https://doi.org/10.1007/978-1-4613-2741-7_1" @default.
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