An exact statistical mechanical derivation is given of the critical Casimir forces for Ising strips with arbitrary surface fields applied to edges. Our results show that the strength as well as the sign of the force can be controlled by varying the temperature or the fields. An interpretation of the results is given in terms of a linked cluster expansion. This suggests a systematic approach for deriving the critical Casimir force which can be used in more general models.
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http://dx.doi.org/10.1103/PhysRevLett.105.055701 | DOI Listing |
Phys Rev E
October 2023
Theoretische Physik der lebenden Materie, Institut für biologische Informationsprozesse (IBI-5), Forschungszentrum Jülich, D-52425 Jülich, Germany.
Density profiles are investigated arising in a critical Ising model in two dimensions which is confined to a rectangular domain with uniform or mixed boundary conditions and arbitrary aspect ratio. For the cases in which the two vertical sides of the rectangle have up-spin boundary conditions + and the two horizontal sides with either down-spin boundary conditions - or with free-spin boundary conditions f, exact results are presented for the density profiles of the energy and the order parameter which display a surprisingly rich behavior. The new results follow by means of conformal transformations from known results in the half plane with +-+-+ and +f+f+ boundary conditions.
View Article and Find Full Text PDFPhys Rev Lett
February 2021
Institute for Theoretical Physics, RWTH Aachen University, 52056 Aachen, Germany.
The exact critical Casimir amplitude is derived for anisotropic systems within the d=2 Ising universality class by combining conformal field theory with anisotropic φ^{4} theory. Explicit results are presented for the general anisotropic scalar φ^{4} model and for the fully anisotropic triangular-lattice Ising model in finite rectangular and infinite strip geometries with periodic boundary conditions. These results demonstrate the validity of multiparameter universality for confined anisotropic systems and the nonuniversality of the critical Casimir amplitude.
View Article and Find Full Text PDFPhys Rev E
January 2021
Theoretical Soft Matter and Biophysics, Institute of Complex Systems, Forschungszentrum Jülich, D-52425 Jülich, Germany.
With conformal-invariance methods, Burkhardt, Guim, and Xue studied the critical Ising model, defined on the upper half plane y>0 with different boundary conditions a and b on the negative and positive x axes. For ab=-+ and f+, they determined the one- and two-point averages of the spin σ and energy ε. Here +,-, and f stand for spin-up, spin-down, and free-spin boundaries, respectively.
View Article and Find Full Text PDFPhys Rev E
May 2017
Department of Physics, Beijing Normal University, Beijing 100875, China.
The two-dimensional Ising model with a slit is studied. The slit free energy is defined, in which the bulk term, edge terms, and corner terms other than that of the slit are canceled. The bond propagation algorithm is used to calculate the free energy, internal energy, and heat capacity numerically.
View Article and Find Full Text PDFJ Chem Phys
June 2016
Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, ul. Pasteura 5, 02-093 Warszawa, Poland.
We consider two-dimensional Ising strip bounded by two planar, inhomogeneous walls. The inhomogeneity of each wall is modeled by a magnetic field acting on surface spins. It is equal to +h1 except for a group of N1 neighboring surface spins where it is equal to -h1.
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