arXiv subjects

Michael Krech

Publications and source records attributed to Michael Krech.

3 recordsLinked to original sources

arXiv2004

The critical Casimir force and its fluctuations in lattice spin models: exact and Monte Carlo results

We present general arguments and construct a stress tensor operator for finite lattice spin models. The average value of this operator gives the Casimir force of the system close to the bulk critical temperature $T_c$. We verify our arguments via exact results for the force in the two-dimensional Ising model, $d$-dimensional Gaussian and mean spherical model with $2 =k_b T_c (d-1)Δ/(L/a)^{d}$, where $L$ is the distance between the plates and $Δ$ is the (universal) Casimir amplitude.

cond-mat.stat-mech↗

arXiv2003

Universality of the thermodynamic Casimir effect

Recently a nonuniversal character of the leading spatial behavior of the thermodynamic Casimir force has been reported [X. S. Chen and V. Dohm, Phys. Rev. E {\bf 66}, 016102 (2002)]. We reconsider the arguments leading to this observation and show that there is no such leading nonuniversal term in systems with short-ranged interactions if one treats properly the effects generated by a sharp momentum cutoff in the Fourier transform of the interaction potential. We also conclude that lattice and continuum models then produce results in mutual agreement independent of the cutoff scheme, contrary to the aforementioned report. All results are consistent with the {\em universal} character of the Casimir force in systems with short-ranged interactions. The effects due to dispersion forces are discussed for systems with periodic or realistic boundary conditions. In contrast to systems with short-ranged interactions, for $L/ξ\gg 1$ one observes leading finite-size contributions governed by power laws in $L$ due to the subleading long-ranged character of the interaction, where $L$ is the finite system size and $ξ$ is the correlation length.

cond-mat.stat-mech↗

arXiv1999

Optimized energy calculation in lattice systems with long-range interactions

We discuss an efficient approach to the calculation of the internal energy in numerical simulations of spin systems with long-range interactions. Although, since the introduction of the Luijten-Blöte algorithm, Monte Carlo simulations of these systems no longer pose a fundamental problem, the energy calculation is still an O(N^2) problem for systems of size N. We show how this can be reduced to an O(N logN) problem, with a break-even point that is already reached for very small systems. This allows the study of a variety of, until now hardly accessible, physical aspects of these systems. In particular, we combine the optimized energy calculation with histogram interpolation methods to investigate the specific heat of the Ising model and the first-order regime of the three-state Potts model with long-range interactions.

cond-mat.stat-mech↗