Functional dimensional regularization applied to the O(N) universality class yields critical exponents comparable to advanced non-perturbative methods while retaining efficiency and rapid convergence.
Critical exponents for 3D O(n)-symmetric model with n > 3
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abstract
Critical exponents for the 3D O(n)-symmetric model with n > 3 are estimated on the base of six-loop renormalization-group (RG) expansions. A simple Pade-Borel technique is used for the resummation of the RG series and the Pade approximants [L/1] are shown to give rather good numerical results for all calculated quantities. For large n, the fixed point location g_c and the critical exponents are also determined directly from six-loop expansions without addressing the resummation procedure. An analysis of the numbers obtained shows that resummation becomes unnecessary when n exceeds 28 provided an accuracy of about 0.01 is adopted as satisfactory for g_c and critical exponents. Further, results of the calculations performed are used to estimate the numerical accuracy of the 1/n-expansion. The same value n = 28 is shown to play the role of the lower boundary of the domain where this approximation provides high-precision estimates for the critical exponents.
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UNVERDICTED 2representative citing papers
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.
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Functional Dimensional Regularization for O(N) Models
Functional dimensional regularization applied to the O(N) universality class yields critical exponents comparable to advanced non-perturbative methods while retaining efficiency and rapid convergence.
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Coherent and dissipative dynamics at quantum phase transitions
A review of equilibrium and dynamic scaling laws at quantum phase transitions, including quenches and dissipative effects treated as perturbations to critical regimes.