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Discontinuities of critical amplitude for specific heat

R. Abe, S. Hikami

Physics Letters AAug 1, 19735 citations

Amplitude ratios and the approach to bulk criticality in parallel plate geometries

Marcelo M. Leite, M. Sardelich, Mauricio D. Coutinho-Filho

We present analytical and numerical results for the specific heat and susceptibility amplitude ratios in parallel plate geometries. The results are derived using field-theoretic techniques suitable to describe the system in the bulk limit, i.e., $(L/{\ensuremath{\xi}}_{\ifmmode\pm\else\textpm\fi{}})\ensuremath{\gg}1,$ where L is the distance between the plates and ${\ensuremath{\xi}}_{\ifmmode\pm\else\textpm\fi{}}$ is the correlation length above (+) and below $(\ensuremath{-})$ the bulk critical temperature. Advantages and drawbacks of our method are discussed in the light of other approaches previously reported in the literature.We present analytical and numerical results for the specific heat and susceptibility amplitude ratios in parallel plate geometries. The results are derived using field-theoretic techniques suitable to describe the system in the bulk limit, i.e., $(L/{\ensuremath{\xi}}_{\ifmmode\pm\else\textpm\fi{}})\ensuremath{\gg}1,$ where L is the distance between the plates and ${\ensuremath{\xi}}_{\ifmmode\pm\else\textpm\fi{}}$ is the correlation length above (+) and below $(\ensuremath{-})$ the bulk critical temperature. Advantages and drawbacks of our method are discussed in the light of other approaches previously reported in the literature.

arXiv:cond-mat/9809052Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsMar 1, 19997 citations

Finite-geometry specific-heat scaling function near the lambda transition

S Bhattacharyya, Jayanta K. Bhattacharjee

Using a technique due to Nicoll for studying the wave-number–dependent specific heat in the bulk geometry, we calculate for temperatures above the lambda point the two-loop specific-heat scaling function for the parallel plate geometry with Dirichlet boundary conditions. We work with the logarithmic specific heat for simplicity, since for the actual superfluid transition the exponent α is very close to zero. The agreement with the recent data is exhibited.

Europhysics Letters (EPL)Jul 15, 19986 citations

On the critical behaviour of the specific heat near four dimensions

C. Bagnuls, Claude Bervillier

Physics Letters AMar 1, 19866 citations

Critical specific heat of systems confined by a wall

Zoran Borjan

Physica A Statistical Mechanics and its ApplicationsDec 12, 20210 citations

Kritische spezifische Wärme in begrenzten Systemen mit Dirichlet-Oberflächen

Ulf Mohr, V. Dohm

The present work investigates the influence of real boundary conditions on the critical behaviour of confined system close to the temperature of a second order phase transition of the bulk. This is done analytically by applying the methods of the field theory of critical phenomena to a half-space geometry with a completely suppressed order parameter on the surface, the so-called Dirichlet boundary conditions. For the first time the surface specific heat is calculated to next to leading order in a fixed dimension both above and below the critical temperature. The results are compared with the data of recent experiments on Helium in plate geometry close to the lambda transition. Apart from the experimentally known bulk amplitudes no adaptable parameters are used. Above the critical temperature a semi-quantitative agreement of theory and experiment is found, whereas the experimental data cannot be explained below the lambda point. Possible reasons for this discrepancy are discussed. Secondly a new method to approximate Dirichlet boundary conditions in Monte Carlo simulations of lattice spin systems is presented. In comparison with established realizations both a better suppression of the order parameter on the boundary and the theoretically predicted scaling behaviour is achieved. Data generated with the new method shows agreement with theory within the expected errors.The present work investigates the influence of real boundary conditions on the critical behaviour of confined system close to the temperature of a second order phase transition of the bulk. This is done analytically by applying the methods of the field theory of critical phenomena to a half-space geometry with a completely suppressed order parameter on the surface, the so-called Dirichlet boundary conditions. For the first time the surface specific heat is calculated to next to leading order in a fixed dimension both above and below the critical temperature. The results are compared with the data of recent experiments on Helium in plate geometry close to the lambda transition. Apart from the experimentally known bulk amplitudes no adaptable parameters are used. Above the critical temperature a semi-quantitative agreement of theory and experiment is found, whereas the experimental data cannot be explained below the lambda point. Possible reasons for this discrepancy are discussed. Secondly a new method to approximate Dirichlet boundary conditions in Monte Carlo simulations of lattice spin systems is presented. In comparison with established realizations both a better suppression of the order parameter on the boundary and the theoretically predicted scaling behaviour is achieved. Data generated with the new method shows agreement with theory within the expected errors.

Jan 1, 20000 citations

Specific heat critical amplitudes and the approach to bulk criticality in parallel plate geometries

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