群C 4v 酉表示中的佯谬

Masafumi Fujimoto, Hiromi Otsuka

We investigate a universal curve in asymptotic correlation functions of off-critical systems that possess C_{6v} symmetry following the argument for C_{4v} symmetry in our previous paper [Phys. Rev. E 102, 032141 (2020)2470-004510.1103/PhysRevE.102.032141]. Unlike the C_{4v} case, a minimal asymptotic form exists, which contains only two free parameters: the normalization constant and the modulus of the universal curve. We perform large-scale Monte Carlo simulations of the triangular lattice Q-state Potts model above the transition temperature. For Q=1, 2, 3, and 4, we successfully obtain numerical evidence that the minimal form gives the leading asymptotic behavior. We also discuss the possibility that the corrections to the minimal form are expressed using this form as a building block. From the minimal form with optimized parameters, we derive the equilibrium crystal shape of the honeycomb lattice Potts model, which is given by an algebraic curve of genus 1 and is universal among models with C_{6v}. Although the curve differs from those obtained in the C_{4v} case, the latter curves also have genus 1. We indicate that the birational equivalence concept can play an important role in comparing asymptotic forms for different point group symmetries, for example, C_{6v} and C_{4v}.

LIU Li, 狄尧民, 刘思平

Hiromi Otsuka, Masafumi Fujimoto

Abstract We focus on asymptotic correlation functions of off-critical models and propose a universal form possessing the C 4v symmetry and that possessing the C 6v symmetry. The former (the latter) is adaptable to classical spin systems on a square (triangular) lattice. Intriguingly, the C 4v form includes three free parameters—an amplitude A , the modulus k , and a deformation parameter b . Meanwhile, the C 6v form does the two of them, i.e., A and k . To proffer numerical evidence to our proposal, we perform large-scale Monte Carlo (MC) simulations of the Q -state Potts models on square and triangular lattices in the paramagnetic phase. We determine the free parameters to fit the forms to the MC data of correlation functions. Then, we find that both universal forms can describe asymptotic behaviors of correlation functions with high accuracy. Also, the C 4v and C 6v forms yield the equilibrium crystal shapes of the square-lattice and honeycomb-lattice models, respectively. These extracted curves of crystal shapes differ, representing the difference of lattice symmetries. Meanwhile, they are both algebraic curves of genus 1 and can become birationally equivalent if the values of k coincide. Our observation indicates that k provides a new measure for comparing the properties of different models on different lattices in two dimensions.

刘惠恩

Eric T. Holland, Yaniv Jacob Rosen, Nicholas Materise +7 more

Investigations into the microwave surface impedance of superconducting resonators have led to the development of single photon counters that rely on kinetic inductance for their operation, while concurrent progress in additive manufacturing, “3D printing,” opens up a previously inaccessible design space for waveguide resonators. In this manuscript, we present results from the synthesis of these two technologies in a titanium, aluminum, vanadium (Ti-6Al-4V) superconducting radio frequency resonator which exploits a design unattainable through conventional fabrication means. We find that Ti-6Al-4V has two distinct superconducting transition temperatures observable in heat capacity measurements. The higher transition temperature is in agreement with DC resistance measurements, while the lower transition temperature, not previously known in the literature, is consistent with the observed temperature dependence of the superconducting microwave surface impedance. From the surface reactance, we extract a London penetration depth of 8 ± 3 μm—roughly an order of magnitude larger than other titanium alloys and several orders of magnitude larger than other conventional elemental superconductors.