A conjecture on the relationship between critical residual entropy and finite temperature pseudo-transitions of one-dimensional models

Recently pseudo-critical temperature clues were observed in one-dimensional spin models, such as the Ising-Heisenberg spin models, among others. Here we report a relationship between the zero-temperature phase boundary residual entropy (critical residual entropy) and pseudo-transition. Usually, the residual entropy increases in the phase boundary, which means the system becomes more degenerate at the phase boundary compared to its adjacent states. However, this is not always the case; at zero temperature, there are some phase boundaries where the entropy holds the largest residual entropy of the adjacent states. Therefore, we can propose the following conjecture: If residual entropy at zero-temperature is a continuous function at least from the one-sided limit at a critical point, then pseudo-transition evidence will appear at finite temperature near the critical point. We expect that this argument would apply to study more realistic models. Only by analyzing the residual entropy at zero temperature, one could identify a priori whether the system will exhibit the pseudo-transition at finite temperature. To strengthen our conjecture, we use two examples of Ising-Heisenberg models, which exhibit pseudo-transition behavior: one frustrated coupled tetrahedral chain and another unfrustrated diamond chain.Comment: 12 pages and 10 figure

Editor\u27s Notes

Since the passing of two high-profile state legislative bills aimed at Arizona\u27s Latino residents this past April, the significance of ethnicity for American citizens has once again surfaced as a topic for national debate. Whether to legitimize, or just as frequently deny, what defines American identity, the question and meaning of one\u27s ethnic roots continues to be a contested matter for many Americans. In particular, HB 2281, a bill targeting the restriction of ethnic studies curricula in Arizona\u27s K- 12 educational system, has prompted accusations that Ethnic Studies scholarship and teachings work against a unified sense of nationhood by encouraging separatism and anti-American sentiment. Yet, as most Ethnic Studies proponents would counter, it is instead the artificial notion of a monolithic American identity, predicated upon a hegemonic rendering of what it is to be an American, that promotes divisions and distrust within a nation. In either case, the ambivalence over how to read the ambiguities of race and ethnicity implicit in U.S. citizenry underscore the ongoing need to address them. As such, the six authors featured in this issue provide fresh and thoughtful examinations of how race and ethnicity complicate understandings of self. Although diverse in content, the articles collectively consider the effects of how the ambivalence of ethnic origins both expand and challenge the meaning of American identity

A Note on High-Energy Scattering of Open Superstrings

We study the Regge and hard scattering limits of the one-loop amplitude for massless open string states in the type I theory. For hard scattering we find the exact coefficient multiplying the known exponential falloff in terms of the scattering angle, without relying on a saddle point approximation for the integration over the cross ratio. This bypasses the issues of estimating the contributions from flat directions, as well as those that arise from fluctuations of the gaussian integration about a saddle point. This result allows for a straightforward computation of the small- angle behavior of the hard scattering regime and we find complete agreement with the Regge limit at high momentum transfer, as expected.Comment: figure added, comments and acknowledgement added, typos correcte

The monotonicity of the apsidal angle using the theory of potential oscillators

In a central force system the angle between two successive passages of a body through pericenters is called the apsidal angle. In this paper we prove that for central forces of the form $f(r)\sim \lambda r^{-(\alpha+1)}$ with $\alpha<2$ the apsidal angle is a monotonous function of the energy, or equivalently of the orbital eccentricity.Comment: 4 page