76 research outputs found
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 . We
verify our arguments via exact results for the force in the two-dimensional
Ising model, -dimensional Gaussian and mean spherical model with . On
the basis of these exact results and by Monte Carlo simulations for
three-dimensional Ising, XY and Heisenberg models we demonstrate that the
standard deviation of the Casimir force in a slab geometry confining a
critical substance in-between is , where is
the surface area of the plates, is the lattice spacing and is a
slowly varying nonuniversal function of the temperature . The numerical
calculations demonstrate that at the critical temperature the force
possesses a Gaussian distribution centered at the mean value of the force
, where is the distance between the
plates and is the (universal) Casimir amplitude.Comment: 21 pages, 7 figures, to appear in PR
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 one observes leading finite-size contributions
governed by power laws in due to the subleading long-ranged character of
the interaction, where is the finite system size and is the
correlation length.Comment: 11 pages, revtex, to appear in Phys. Rev. E 68 (2003
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-Bl\"ote 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.Comment: 10 pages, including 8 EPS figures. To appear in Phys. Rev. E. Also
available as PDF file at
http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm
Short-time scaling behavior of growing interfaces
The short-time evolution of a growing interface is studied within the
framework of the dynamic renormalization group approach for the
Kadar-Parisi-Zhang (KPZ) equation and for an idealized continuum model of
molecular beam epitaxy (MBE). The scaling behavior of response and correlation
functions is reminiscent of the ``initial slip'' behavior found in purely
dissipative critical relaxation (model A) and critical relaxation with
conserved order parameter (model B), respectively. Unlike model A the initial
slip exponent for the KPZ equation can be expressed by the dynamical exponent
z. In 1+1 dimensions, for which z is known exactly, the analytical theory for
the KPZ equation is confirmed by a Monte-Carlo simulation of a simple ballistic
deposition model. In 2+1 dimensions z is estimated from the short-time
evolution of the correlation function.Comment: 27 pages LaTeX with epsf style, 4 figures in eps format, submitted to
Phys. Rev.
AAPT Diagnostic Criteria for Chronic Cancer Pain Conditions
Chronic cancer pain is a serious complication of malignancy or its treatment. Currently, no comprehensive, universally accepted cancer pain classification system exists. Clarity in classification of common cancer pain syndromes would improve clinical assessment and management. Moreover, an evidence-based taxonomy would enhance cancer pain research efforts by providing consistent diagnostic criteria, ensuring comparability across clinical trials. As part of a collaborative effort between the Analgesic, Anesthetic, and Addiction Clinical Trial Translations Innovations Opportunities and Networks (ACTTION) and the American Pain Society (APS), the ACTTION-APS Pain Taxonomy (AAPT) initiative worked to develop the characteristics of an optimal diagnostic system.59, 65 Following the establishment of these characteristics, a working group consisting of clinicians and clinical and basic scientists with expertise in cancer and cancer-related pain was convened to generate core diagnostic criteria for an illustrative sample of 3 chronic pain syndromes associated with cancer (i.e., bone pain and pancreatic cancer pain as models of pain related to a tumor) or its treatment (i.e., chemotherapy-induced peripheral neuropathy). A systematic review and synthesis was conducted to provide evidence for the dimensions that comprise this cancer pain taxonomy. Future efforts will subject these diagnostic categories and criteria to systematic empirical evaluation of their feasibility, reliability and validity and extension to other cancer-related pain syndromes
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