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- W2052029941 startingPage "3523" @default.
- W2052029941 abstract "The thermodynamic functions of an $n$-component $d$-dimensional ${ensuremath{sigma}}^{4}$ theory are written in the form ${f}_{i}={A}_{i}{|t|}^{ensuremath{-}{ensuremath{lambda}}_{i}}(1+{a}_{i}{|t|}^{ensuremath{Delta}})$, where $t=frac{(Tensuremath{-}{T}_{c})}{{T}_{c}}$. The correction-to-scaling amplitudes ${a}_{i}$ are calculated to leading order in $frac{1}{n}$ for $2<d<4$, and the universality of their ratios is explicitly shown. The effective exponents ${ensuremath{lambda}}_{i,mathrm{eff}}={ensuremath{lambda}}_{i}ensuremath{-}{a}_{i}ensuremath{Delta}{|t|}^{ensuremath{Delta}}$ violate the thermodynamic scaling laws already at this leading order. The amplitudes ${a}_{i}$ have singularities (as functions of $d$) at the dimensionalities ${stackrel{ifmmode tilde{}else ~{}fi{}}{d}}_{l}=2+frac{4}{l},l=3,4,5,dots{}$. Above ${T}_{c}$, the specific heat and the susceptibility correction amplitudes ${a}_{c}^{+}$ and ${a}_{ensuremath{chi}}^{+}$ are discontinuous at ${stackrel{ifmmode tilde{}else ~{}fi{}}{d}}_{l}$ and at ${stackrel{ifmmode tilde{}else ~{}fi{}}{d}}_{2l}(lensuremath{ge}2)$, respectively. Below ${T}_{c}$, the magnetization and the stiffness correction amplitudes are zero, ${a}_{M}={a}_{{ensuremath{rho}}_{s}}=0$, while ${a}_{c}^{ensuremath{-}}$ diverges at ${stackrel{ifmmode tilde{}else ~{}fi{}}{d}}_{2l+1}(lensuremath{ge}1)$ but is continuous at ${d}_{2l}$ (in particular at $d=3$). Results are also given for universal ratios among corrections-to-scaling amplitudes for the dependence of thermo-dynamic functions on the magnetization at $T={T}_{c}$ and at a nonzero field." @default.
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- W2052029941 date "1981-04-01" @default.
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- W2052029941 title "Universal ratios among corrections-to-scaling amplitudes in the large-nlimit" @default.
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- W2052029941 doi "https://doi.org/10.1103/physrevb.23.3523" @default.
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