Universality and nonmonotonic finite-size effects above the upper critical dimension

Abstract

We analyze universal and nonuniversal finite-size effects of lattice systems in a $L^d$ geometry above the upper critical dimension d = 4 within the O(n) symmetric ${\varphi }^4$ lattice theory. On the basis of exact results for $n\to \infty$ and one-loop results for n = 1 we identify significant lattice effects that cannot be explained by the ${\varphi }^4$ continuum theory. Our analysis resolves longstanding discrepancies between earlier asymptotic theories and Monte Carlo (MC) data for the five-dimensional Ising model of small size. We predict a {\it nonmonotonic} L dependence of the scaled susceptibility $\chi L^{-d/2}$ at $T_c$ with a weak maximum that has not yet been detected by MC data.

LaTex, 4 pages, submitted to Phys. Rev. Lett

References in corpus (4)

• Finite-size scaling above the upper critical dimension revisited: The case of the five-dimensional Ising model
• Monte Carlo investigations of phase transitions: status and perspectives
• Relation between bulk order-parameter correlation function and finite-size scaling
• Lattice ${\varphi }^4$ theory of finite-size effects above the upper critical dimension

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• Crossover from low-temperature to high-temperature fluctuations. II. Nonuniversal thermodynamic Casimir forces of anisotropic systems
• Crossover from low-temperature to high-temperature fluctuations. I. Thermodynamic Casimir forces of isotropic systems
• Finite-size scaling of directed percolation in the steady state
• Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions
• Finite-size scaling of the d=5 Ising model embedded in the cylindrical geometry: An influence of the hyperscaling violation
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions