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Boris Kastening

Publications and source records attributed to Boris Kastening.

At least 19 recordsLinked to original sources
arXiv2013

Anisotropy and universality: Critical Binder cumulant of the two-dimensional Ising model

We reanalyze transfer matrix and Monte Carlo results for the critical Binder cumulant U* of an anisotropic two-dimensional Ising model on a square lattice in a square geometry with periodic boundary conditions. Spins are coupled between nearest neighboring sites and between next-nearest neighboring sites along one of the lattice diagonals. We find that U* depends only on the asymptotic critical long-distance features of the anisotropy, irrespective of its realization through ferromagnetic or antiferromagnetic next-nearest neighbor couplings. We modify an earlier renormalization-group calculation to obtain a quantitative description of the anisotropy dependence of U*. Our results support our recent claim towards the validity of universality for critical phenomena in the presence of a weak anisotropy.

cond-mat.stat-mech↗
arXiv2012

Universal anisotropic finite-size critical behavior of the two-dimensional Ising model on a strip and of d-dimensional models on films

Anisotropy effects on the finite-size critical behavior of a two-dimensional Ising model on a general triangular lattice in an infinite-strip geometry with periodic, antiperiodic, and free boundary conditions (bc) in the finite direction are investigated. Exact results are obtained for the scaling functions of the finite-size contributions to the free energy density. With xi_> the largest and xi_< the smallest bulk correlation length at a given temperature near criticality, we find that the dependence of these functions on the ratio xi_< / xi_> and on the angle parameterizing the orientation of the correlation volume is of geometric rather than dynamic origin. Since the scaling functions are independent of the particular microscopic realization of the anisotropy within the two-dimensional Ising model, our results provide a limited verification of universality. We explain our observations by considering finite-size scaling of free energy densities of general weakly anisotropic models on a d-dimensional film, i.e., in an L x infinity^(d-1) geometry, with bc in the finite direction that are invariant under a shear transformation relating the anisotropic and isotropic cases. This allows us to relate free energy scaling functions in the presence of an anisotropy to those of the corresponding isotropic system. We interpret our results as a simple and transparent case of anisotropic universality, where, compared to the isotropic case, scaling functions depend additionally on the shape and orientation of the correlation volume. We conjecture that this universality extends to cases where the geometry and/or the bc are not invariant under the shear transformation and argue in favor of validity of two-scale factor universality for anisotropic systems.

cond-mat.stat-mech↗
arXiv2010

Finite-size effects in film geometry with nonperiodic boundary conditions: Gaussian model and renormalization-group theory at fixed dimension

Finite-size effects are investigated in the Gaussian model with isotropic and anisotropic short-range interactions in film geometry with nonperiodic boundary conditions (b.c). We have obtained exact results for the free energy and the Casimir force for antiperiodic, Neumann, Dirichlet, and Neumann-Dirichlet mixed b.c. in 1<d<4 dimensions. For the Casimir force, finite-size scaling is found to be valid for all b.c.. For the free energy, finite-size scaling is valid in 1<d<3 and 3<d<4 dimensions for antiperiodic, Neumann, and Dirichlet b.c., but logarithmic deviations from finite-size scaling exist in d=3 dimensions for Neumann and Dirichlet b.c.. This is explained in terms of the borderline dimension d*=3, where the critical exponent of the Gaussian surface energy density vanishes. For Neumann-Dirichlet b.c., finite-size scaling is strongly violated above T_c for 1<d<4. Our results include an exact description of the dimensional crossover between the d-dimensional finite-size critical behavior near bulk T_c and the (d-1)-dimensional critical behavior near T_c,film(L). This dimensional crossover is illustrated for the critical behavior of the specific heat. For 2<d<4, the Gaussian results are reformulated as one-loop contributions of the phi^4 theory at fixed dimension and are compared with the epsilon=4-d expansion results as well as with d=3 Monte Carlo data. For d=2, the Gaussian results for the Casimir force scaling function are compared with those for the Ising model; unexpected exact relations are found between the Gaussian and Ising scaling functions. For both the Gaussian and the Ising model it is shown that anisotropic couplings imply nonuniversal scaling functions of the Casimir force. Our Gaussian results provide the basis for the investigation of finite-size effects of the mean spherical model with nonperiodic b.c..

cond-mat.stat-mech↗
arXiv2009

Charge Transport and Quantum Phase Transitions in Singlet Superconductor - Ferromagnet - Singlet Superconductor Junctions

We study the Josephson current, I_J, in a junction consisting of two s-wave superconductors that are separated by a ferromagnetic barrier possessing a magnetic and non-magnetic scattering potential, g and Z, respectively. We discuss the general dependence of I_J on g, Z, and the phase difference ϕbetween the two superconductors. Moreover, we compute the critical current, I_c for given g and Z, and show that it possesses two lines of non-analyticity in the (g, Z)-plane. We identify those regions in the (g, Z)-plane where the Josephson current changes sign with increasing temperature without a change in the relative phase between the two superconductors, i.e., without a transition between a 0 and πstate of the junction. Finally, we show that by changing the relative phase ϕ, it is possible to tune the junction through a first-order quantum phase transition in which the spin polarization of the two superconductors' combined ground state changes from < S_z > =0 to < S_z > =1/2.

cond-mat.supr-con↗
arXiv2007

Interplay of ferromagnetism and triplet superconductivity in a Josephson junction

In this paper we extend our earlier analysis of the novel Josephson effect in triplet superconductor--ferromagnet--triplet superconductor (TFT) junctions [B. Kastening \emph{et al.}, Phys. Rev. Lett. {\bf{96}}, 047009 (2006)]. In our more general formulation of the TFT junction we allow for potential scattering at the barrier and an arbitrary orientation of the ferromagnetic moment. Several new effects are found upon the inclusion of these extra terms: for example, we find that a Josephson current can flow even when there is vanishing phase difference between the superconducting condensates on either side of the barrier. The critical current for a barrier with magnetization parallel to the interface is calculated as a function of the junction parameters, and is found to display strong non-analyticities. Furthermore, the Josephson current switches first identified in our previous work are found to be robust features of the junction, while the unconventional temperature-dependence of the current is very sensitive to the extra terms in the barrier Hamiltonian.

cond-mat.supr-con↗
arXiv2006

Fluctuation pressure of a fluid membrane between walls through six loops

The fluctuation pressure that an infinitely extended fluid membrane exerts on two enclosing parallel hard walls is computed. Variational perturbation theory is used to extract the hard-wall limit from a perturbative expansion through six loops obtained with a smooth wall potential. Our result alpha=0.0821+/-0.0005 for the constant conventionally parametrizing the pressure lies above earlier Monte Carlo results.

cond-mat.stat-mech↗
arXiv2005

Pedestrian Solution of the Two-Dimensional Ising Model

The partition function of the two-dimensional Ising model with zero magnetic field on a square lattice with m x n sites wrapped on a torus is computed within the transfer matrix formalism in an explicit step-by-step approach inspired by Kaufman's work. However, working with two commuting representations of the complex rotation group SO(2n,C) helps us avoid a number of unnecessary complications. We find all eigenvalues of the transfer matrix and therefore the partition function in a straightforward way.

cond-mat.stat-mech↗
arXiv2005

Novel Josephson Effect in Triplet Superconductor - Ferromagnet - Triplet Superconductor Junctions

We predict a novel type of Josephson effect to occur in triplet superconductor - ferromagnet - triplet superconductor Josephson junctions. We show that the Josephson current, I_J, exhibits a rich dependence on the relative orientation between the ferromagnetic moment and the d-vectors of the superconductors. This dependence can be used to build several types of Josephson current switches. Moreover, we predict an unconventional temperature dependence of I_J in which I_J changes sign with increasing temperature

cond-mat.supr-con↗
arXiv2004

Non-universal Critical Quantities from Variational Perturbation Theory and Their Application to the BEC Temperature Shift

For an O(N) symmetric scalar field theory with Euclidean action integral d^3x [1/2 |nabla phi|^2 + 1/2 r phi^2 + 1/4! u phi^4], where phi = (phi_1,...,phi_N) is a vector of N real field components, variational perturbation theory through seven loops is employed for N = 0,1,2,3,4 to compute the renormalized value of r/(N+2)u^2 at the phase transition. Its exact large-N limit is determined as well. We also extend an earlier computation of the interaction-induced shift Delta /Nu for N = 1,2,4 to N = 0,3. For N = 2, the results for the two quantities are used to compute the second-order shift of the condensation temperature of a dilute Bose gas, both in the homogenous case and for the wide limit of a harmonic trap. Our results are in agreement with earlier Monte Carlo simulations for N = 1,2,4. The appendix contains previously unpublished numerical seven-loop data provided to us by B.Nickel.

cond-mat.stat-mech↗
arXiv2004

Shift of BEC Temperature of Homogenous Weakly Interacting Bose Gas

We report on the computation of the shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the diluteness parameter a n^(1/3), where `a' is the scattering length and `n' is the particle density. The perturbative series, which is afflicted by infrared divergences, is resummed by means of variational perturbation theory. Using coefficients through seven loops, we arrive at Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3), which compares favorably with recent Monte-Carlo data.

cond-mat.stat-mech↗
arXiv2003

Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops

The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length `a' is computed for given particle density `n.' Variational perturbation theory is used to resum the corresponding perturbative series for Delta /Nu in a classical three-dimensional scalar field theory with coupling `u' and where the physical case of N=2 field components is generalized to arbitrary N. Our results for N=1,2,4 are in agreement with recent Monte-Carlo simulations; for N=2, we obtain Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use seven-loop perturbative coefficients, extending earlier work by one loop order.

cond-mat.stat-mech↗
arXiv2003

Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops

We compute the shift of the transition temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length a for given particle density n. Using variational perturbation theory through six loops in a classical three-dimensional scalar field theory, we obtain Delta T_c/T_c = 1.25+/-0.13 a n^(1/3), in agreement with recent Monte-Carlo results.

cond-mat.stat-mech↗
arXiv2003

Fluctuation Pressure of a Membrane Between Walls Through Five Loops

An earlier four-loop calculation of the fluctuation pressure of a fluid membrane between two infinite walls is extended to five loops. Variational perturbation theory is used to extract the hard-wall limit from perturbative results obtained with a smooth potential. Comparison with a structurally similar quantum mechanics problem of a particle in a box is used for an alternative way of extracting the membrane pressure and also to estimate the quality of the results. Our values lie above the best available Monte Carlo data.

cond-mat.stat-mech↗
arXiv2002

Simplified Transfer Matrix Approach in the Two-Dimensional Ising Model with Various Boundary Conditions

A recent simplified transfer matrix solution of the two-dimensional Ising model on a square lattice with periodic boundary conditions is generalized to periodic-antiperiodic, antiperiodic-periodic and antiperiodic-antiperiodic boundary conditions. It is suggested to employ linear combinations of the resulting partition functions to investigate finite-size scaling. An exact relation of such a combination to the partition function corresponding to Brascamp-Kunz boundary conditions is found.

cond-mat.stat-mech↗
arXiv2002

Three-Loop Ground-State Energy of O(N)-Symmetric Ginzburg-Landau Theory Above T_c in 4-epsilon Dimensions with Minimal Subtraction

As a step towards deriving universal amplitude ratios of the superconductive phase transition we calculate the vacuum energy density in the symmetric phase of O(N)-symmetric scalar QED in D=4-epsilon dimensions in an epsilon-expansion using the minimal subtraction scheme commonly denoted by MS-bar. From the diverging parts of the diagrams, we obtain the renormalization constant of the vacuum Z_v which also contains information on the critical exponent alpha of the specific heat. As a side result, we use an earlier two-loop calculation of the effective potential (H.K. and B.VdB., Phys.Rev. E63 (2001) 056113, cond-mat/0104102) to determine the renormalization constant of the scalar field Z_phi up to two loops.

cond-mat.stat-mech↗
arXiv2000

Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy

The free energy of a multi-component scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys non-linear functional differential equations which are turned into recursion relations for the connected Greens functions in a loop expansion. These relations amount to a simple proof that W[G,J] generates only connected graphs and can be used to find all such graphs with their combinatoric weights. A Legendre transformation with respect to the external current converts the functional differential equations for the free energy into those for the effective energy Gamma[G,Phi], which is considered as a functional of the free correlation function G and the field expectation Phi. These equations are turned into recursion relations for the one-particle irreducible Greens functions. These relations amount to a simple proof that Gamma[G,J] generates only one-particle irreducible graphs and can be used to find all such graphs with their combinatoric weights. The techniques used also allow for a systematic investigation into resummations of classes of graphs. Examples are given for resumming one-loop and multi-loop tadpoles, both through all orders of perturbation theory. Since the functional differential equations derived are non-perturbative, they constitute also a convenient starting point for other expansions than those in numbers of loops or powers of coupling constants. We work with general interactions through four powers in the field.

hep-th↗
arXiv1999

Resonance in Strong WW Rescattering in Massive SU(2) Gauge Theory

We investigate the effects of WW rescattering through strong anomalous four-vector boson couplings. In the I=1, J=1 channel, we find a resonance with a mass of approximately 200 GeV and a width of less than 12 GeV. In an application to pion physics we find a small correction to the KSRF relation.

hep-ph↗