Finite-size scaling behavior in trapped systems

Abstract

Numerical transfer-matrix methods are applied to two-dimensional Ising spin systems, in presence of a confining magnetic field which varies with distance $|\vec{x}|$ to a "trap center", proportionally to $(|\vec{x}|/\ell {)}^p$, $p>0$. On a strip geometry, the competition between the "trap size" $\ell$ and the strip width, $L$, is analysed in the context of a generalized finite-size scaling {\em ansatz}. In the low-field regime $\ell \gg L$, we use conformal-invariance concepts in conjunction with a linear-response approach to derive the appropriate ($p$-dependent) limit of the theory, which agrees very well with numerical results for magnetization profiles. For high fields $\ell \lesssim L$, correlation-length scaling data broadly confirms an existing picture of $p$-dependent characteristic exponents. Standard spin-1/2 and spin-1 Ising systems are considered, as well as the Blume-Capel model.

RevTeX, 8 pages, 7 .eps figures (published version

References in corpus (3)

• Many-Body Physics with Ultracold Gases
• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• On locations and properties of the multicritical point of Gaussian and +/-J Ising spin glasses

Cited by in corpus (9)

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• Renormalization-group flow and asymptotic behaviors at the Berezinskii-Kosterlitz-Thouless transitions
• Critical parameters from trap-size scaling in trapped particle systems
• Smoothly-varying hopping rates in driven flow with exclusion
• OPE Coefficients of the 3D Ising model with a trapping potential
• Dimensional crossover of Bose-Einstein condensation phenomena in quantum gases confined within slab geometries
• Universal scaling of three-dimensional bosonic gases in a trapping potential
• Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions
• Critical behavior at the spatial boundary of a trapped inhomogeneous Bose-Einstein condensate