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Constant Magnetic Field (constant + magnetic_field)
Selected AbstractsField theory on a non-commutative plane: a non-perturbative studyFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 5 2004F. Hofheinz Abstract The 2d gauge theory on the lattice is equivalent to the twisted Eguchi,Kawai model, which we simulated at N ranging from 25 to 515. We observe a clear large N scaling for the 1- and 2-point function of Wilson loops, as well as the 2-point function of Polyakov lines. The 2-point functions agree with a universal wave function renormalization. The large N double scaling limit corresponds to the continuum limit of non-commutative gauge theory, so the observed large N scaling demonstrates the non-perturbative renormalizability of this non-commutative field theory. The area law for the Wilson loops holds at small physical area as in commutative 2d planar gauge theory, but at large areas we find an oscillating behavior instead. In that regime the phase of the Wilson loop grows linearly with the area. This agrees with the Aharonov-Bohm effect in the presence of a constant magnetic field, identified with the inverse non-commutativity parameter. Next we investigate the 3d ,,4 model with two non-commutative coordinates and explore its phase diagram. Our results agree with a conjecture by Gubser and Sondhi in d = 4, who predicted that the ordered regime splits into a uniform phase and a phase dominated by stripe patterns. We further present results for the correlators and the dispersion relation. In non-commutative field theory the Lorentz invariance is explicitly broken, which leads to a deformation of the dispersion relation. In one loop perturbation theory this deformation involves an additional infrared divergent term. Our data agree with this perturbative result. We also confirm the recent observation by Ambjø rn and Catterall that stripes occur even in d = 2, although they imply the spontaneous breaking of the translation symmetry. [source] Weak asymptotics of the spectral shift functionMATHEMATISCHE NACHRICHTEN, Issue 11 2007Vincent Bruneau Abstract We consider the three-dimensional Schrödinger operator with constant magnetic field of strength b > 0, and with smooth electric potential. The weak asymptotics of the spectral shift function with respect to b , +, is studied. First, we fix the distance to the Landau levels, then the distance to Landau levels tends to infinity as b , +,. In particular we give explicitly the leading terms in the asymptotics and in some case we obtain full asymptotics expansions. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] One-dimensional disordered magnetic Ising systems: A new approachPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 9 2009Vladimir Gasparian Abstract We reconsider the problem of a one-dimensional Ising model with an arbitrary nearest-neighbor random exchange integral, temperature, and random magnetic field in each site. A convenient formalism is developed that reduces the partition function to a recurrence equation, which is convenient both for numerical as well as for analytical approaches. We have calculated asymptotic expressions for an ensemble averaged free energy and the averaged magnetization in the case of strong and weak couplings in external constant magnetic field. With a random magnetic field at each site in addition to nearest-neighbor random exchange integrals we also evaluated the free energy. We show that the zeros of the partition function for the Ising model in the complex external magnetic field plane formally coincide with the singularities of the real part of electron's transmission amplitude through the chain of , -function potentials. [source] On the Ginzburg-Landau critical field in three dimensionsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 2 2009S. Fournais We study the three-dimensional Ginzburg-Landau model of superconductivity. Several "natural" definitions of the (third) critical field, H, governing the transition from the superconducting state to the normal state, are considered. We analyze the relation between these fields and give conditions as to when they coincide. An interesting part of the analysis is the study of the monotonicity of the ground state energy of the Laplacian with constant magnetic field and with Neumann (magnetic) boundary condition in a domain ,. It is proved that the ground state energy is a strictly increasing function of the field strength for sufficiently large fields. As a consequence of our analysis, we give an affirmative answer to a conjecture by Pan. © 2008 Wiley Periodicals, Inc. [source] | |||||||||||||