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 (1)

• Smoothly-varying hopping rates in driven flow with exclusion