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Register a new userNumerical evidence of conformal phase transition in graphene with long-range interactions
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Using state of the art Hybrid-Monte-Carlo (HMC) simulations we carry out an unbiased study of the competition between spin-density wave (SDW) and charge-density wave (CDW) order in suspended graphene. We determine that the realistic inter-electron potential of graphene must be scaled up by a factor of roughly 1.6 to induce a semimetal-SDW phase transition and find no evidence for CDW order. A study of critical properties suggests that the universality class of the three-dimensional chiral Heisenberg Gross-Neveu model with two fermion flavors, predicted by renormalization group studies and strong-coupling expansion, is unlikely to apply to this transition. We propose that our results instead favor an interpretation in terms of a conformal phase transition. In addition, we describe a variant of the HMC algorithm which uses exact fermionic forces during molecular dynamics trajectories and avoids the use of pseudofermions. Compared to standard HMC this allows for a substantial increase of the integrator stepsize while achieving comparable Metropolis acceptance rates and leads to a sizable performance improvement.
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Ultrathin magnetic films can be modeled as an anisotropic Heisenberg model with long range dipolar interactions. It is believed that the phase diagram presents three phases: A ordered ferromagnetic phase (I), a phase characterized by a change from out-of-plane to in-plane in the magnetization (II), and a high temperature paramagnetic phase (III). It is claimed that the border lines from phase I to III and II to III are of second order and from I to II is first order. In the present work we have performed a very careful Monte Carlo simulation of the model. Our results strongly support that the line separating phase II and III is of the BKT type.
The conception of the conformal phase transiton (CPT), which is relevant for the description of non-perturbative dynamics in gauge theories, is introduced and elaborated. The main features of such a phase transition are established. In particular, it is shown that in the CPT there is an abrupt change of the spectrum of light excitations at the critical point, though the phase transition is continuous. The structure of the effective action describing the CPT is elaborated and its connection with the dynamics of the partially conserved dilatation current is pointed out. The applications of these results to QCD, models of dynamical electroweak symmetry breaking, and to the description of the phase diagram in (3+1)-dimensional $ SU(N_c)$ gauge theories are considered.
In this work we have used extensive Monte Carlo calculations to study the planar to paramagnetic phase transition in the two-dimensional anisotropic Heisenberg model with dipolar interactions (AHd) considering the true long-range character of the dipolar interactions by means of the Ewald summation. Our results are consistent with an order-disorder phase transition with unusual critical exponents in agreement with our previous results for the Planar Rotator model with dipolar interactions. Nevertheless, our results disagrees with the Renormalization Group results of Maier and Schwabl [PRB, 70, 134430 (2004)] and the results of Rapini et. al. [PRB, 75, 014425 (2007)], where the AHd was studied using a cut-off in the evaluation of the dipolar interactions. We argue that besides the long-range character of dipolar interactions their anisotropic character may have a deeper effect in the system than previously believed. Besides, our results shows that the use of a cut-off radius in the evaluation of dipolar interactions must be avoided when analyzing the critical behavior of magnetic systems, since it may lead to erroneous results.
We study the spectrum of the long-range supersymmetric su$(m)$ $t$-$J$ model of Kuramoto and Yokoyama in the presence of an external magnetic field and a charge chemical potential. To this end, we first establish the precise equivalence of a large class of models of this type to a family of su$(1|m)$ spin chains with long-range exchange interactions and a suitable chemical potential term. We exploit this equivalence to compute in closed form the partition function of the long-range $t$-$J$ model, which we then relate to that of an inhomogeneous vertex model with simple interactions. From the structure of this partition function we are able to deduce an exact formula for the restricted partition function of the long-range $t$-$J$ model in subspaces with well-defined magnon content in terms of its analogue for the equivalent vertex model. This yields a complete analytical description of the spectrum in the latter subspaces, including the precise degeneracy of each level, by means of the supersymmetric version of Haldanes motifs and their related skew Young tableaux. As an application, we determine the structure of the motifs associated with the ground state of the spin $1/2$ model in the thermodynamic limit in terms of the magnetic field strength and the charge chemical potential. This leads to a complete characterization of the distinct ground state phases, determined by their spin content, in terms of the magnetic field strength and the charge chemical potential.
Recent theoretical studies [Chen et al., Phys. Rev. B 82, 174440 (2010), Ishizuka et al., Phys. Rev. B 90, 184422 (2014)] for the magnetic Mott insulator Ba2NaOsO6 have proposed a low-temperature order parameter that breaks lattice rotational symmetry without breaking time reversal symmetry leading to a nematic phase just above magnetic ordering temperature. We present high-resolution calorimetric and magnetization data of the same Ba2NaOsO6 single crystal and show evidence for a weakly field-dependent phase transition occurring at a temperature of Ts ~ 9.5K, above the magnetic ordering temperature of Tc ~ 7.5K. This transition appears as a broadened step in the low-field temperature dependence of the specific heat. The evolution of the phase boundary with applied magnetic field suggests that this phase coincides with the phase of broken local point symmetry seen in high field NMR experiments [Lu et al., Nat. Comm. 8 14407 (2017)]. Furthermore, the magnetic field dependence of the specific heat provides clear indications for magnetic correlations persisting at temperatures between Tc and Ts where long-range magnetic order is absent giving support for the existence of the proposed nematic phase.
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