Critical frontier of the triangular antiferromagnet in a field

We study the critical line of the triangular Ising antiferromagnet in an external magnetic field by means of a finite-size analysis of results obtained by transfer-matrix and Monte Carlo techniques. We compare the shape of the critical line with predictions of two different theoretical scenarios. Both scenarios, while plausible, involve assumptions. The first scenario is based on the generalization of the model to a vertex model, and the assumption that the exact analytic form of the critical manifold of this vertex model is determined by the zeroes of an O(2) gauge-invariant polynomial in the vertex weights. However, it is not possible to fit the coefficients of such polynomials of orders up to 10, such as to reproduce the numerical data for the critical points. The second theoretical prediction is based on the assumption that a renormalization mapping exists of the Ising model on the Coulomb gas, and analysis of the resulting renormalization equations. It leads to a shape of the critical line that is inconsistent with the first prediction, but consistent with the numerical data.Comment: 13 pages, 9 figure

Critical behavior of 2 and 3 dimensional ferro- and antiferromagnetic spin ice systems in the framework of the Effective Field Renormalization Group technique

In this work we generalize and subsequently apply the Effective Field Renormalization Group technique to the problem of ferro- and antiferromagnetically coupled Ising spins with local anisotropy axes in geometrically frustrated geometries (kagome and pyrochlore lattices). In this framework, we calculate the various ground states of these systems and the corresponding critical points. Excellent agreement is found with exact and Monte Carlo results. The effects of frustration are discussed. As pointed out by other authors, it turns out that the spin ice model can be exactly mapped to the standard Ising model but with effective interactions of the opposite sign to those in the original Hamiltonian. Therefore, the ferromagnetic spin ice is frustrated, and does not order. Antiferromagnetic spin ice (in both 2 and 3 dimensions), is found to undergo a transition to a long range ordered state. The thermal and magnetic critical exponents for this transition are calculated. It is found that the thermal exponent is that of the Ising universality class, whereas the magnetic critical exponent is different, as expected from the fact that the Zeeman term has a different symmetry in these systems. In addition, the recently introduced Generalized Constant Coupling method is also applied to the calculation of the critical points and ground state configurations. Again, a very good agreement is found with both exact, Monte Carlo, and renormalization group calculations for the critical points. Incidentally, we show that the generalized constant coupling approach can be regarded as the lowest order limit of the EFRG technique, in which correlations outside a frustrated unit are neglected, and scaling is substituted by strict equality of the thermodynamic quantities.Comment: 28 pages, 9 figures, RevTeX 4 Some minor changes in the conclussions. One reference adde

An action for the exact string black hole

A local action is constructed describing the exact string black hole discovered by Dijkgraaf, Verlinde and Verlinde in 1992. It turns out to be a special 2D Maxwell-dilaton gravity theory, linear in curvature and field strength. Two constants of motion exist: mass M>1, determined by the level k, and U(1)-charge Q>0, determined by the value of the dilaton at the origin. ADM mass, Hawking temperature T_H \propto \sqrt{1-1/M} and Bekenstein-Hawking entropy are derived and studied in detail. Winding/momentum mode duality implies the existence of a similar action, arising from a branch ambiguity, which describes the exact string naked singularity. In the strong coupling limit the solution dual to AdS_2 is found to be the 5D Schwarzschild black hole. Some applications to black hole thermodynamics and 2D string theory are discussed and generalizations - supersymmetric extension, coupling to matter and critical collapse, quantization - are pointed out.Comment: 41 pages, 2 eps figures, dedicated to Wolfgang Kummer on occasion of his Emeritierung; v2: added ref; v3: extended discussion in sections 3.2, 3.3 and at the end of 5.3 by adding 2 pages of clarifying text; updated refs; corrected typo