Determining efficient temperature sets for the simulated tempering method

In statistical physics, the efficiency of tempering approaches strongly depends on ingredients such as the number of replicas $R$, reliable determination of weight factors and the set of used temperatures, ${\mathcal T}_R = \{T_1, T_2, \ldots, T_R\}$. For the simulated tempering (SP) in particular -- useful due to its generality and conceptual simplicity -- the latter aspect (closely related to the actual $R$) may be a key issue in problems displaying metastability and trapping in certain regions of the phase space. To determine ${\mathcal T}_R$'s leading to accurate thermodynamics estimates and still trying to minimize the simulation computational time, here it is considered a fixed exchange frequency scheme for the ST. From the temperature of interest $T_1$, successive $T$'s are chosen so that the exchange frequency between any adjacent pair $T_r$ and $T_{r+1}$ has a same value $f$. By varying the $f$'s and analyzing the ${\mathcal T}_R$'s through relatively inexpensive tests (e.g., time decay toward the steady regime), an optimal situation in which the simulations visit much faster and more uniformly the relevant portions of the phase space is determined. As illustrations, the proposal is applied to three lattice models, BEG, Bell-Lavis, and Potts, in the hard case of extreme first-order phase transitions, always giving very good results, even for $R=3$. Also, comparisons with other protocols (constant entropy and arithmetic progression) to choose the set ${\mathcal T}_R$ are undertaken. The fixed exchange frequency method is found to be consistently superior, specially for small $R$'s. Finally, distinct instances where the prescription could be helpful (in second-order transitions and for the parallel tempering approach) are briefly discussed.Comment: 10 pages, 14 figure

General approach for studying first-order phase transitions at low temperatures

By combining different ideas, a general and efficient protocol to deal with discontinuous phase transitions at low temperatures is proposed. For small $T$'s, it is possible to derive a generic analytic expression for appropriate order parameters, whose coefficients are obtained from simple simulations. Once in such regimes simulations by standard algorithms are not reliable, an enhanced tempering method, the parallel tempering -- accurate for small and intermediate system sizes with rather low computational cost -- is used. Finally, from finite size analysis, one can obtain the thermodynamic limit. The procedure is illustrated for four distinct models, demonstrating its power, e.g., to locate coexistence lines and the phases density at the coexistence.Comment: 5 page

The Emerging Legal Architecture for Social Justice

Lawyers advocating for social change are now front and center in newspapers and social media. This article discusses how a new breed of progressive lawyers envision social justice law practice today. These “critical lawyers” are diverse in background, gender, ethnicity and race. They see law as a complex, contradictory tool rather than a necessary and sufficient route to justice. Their practices differ from the traditional non-profit public interest firms of the earlier generation that assumed justice would result if law and lawyers were accessible. To highlight the differences, the article discusses the law practices of Beyond Legal Aid, Law for Black Lives, and TIME’s UP. Beyond Legal Aid is redesigning legal services to produce community partnerships. Law for Black Lives provides legal services to ensure greater equity in criminal procedures. TIME’s UP is radically revising how women respond to sexual harassment at the workplace. These practices seek to democratize the use of law to advance social justice by developing community and client collaborations. The practices rely on revenue from many sources including client fees, small donations through on-line platforms, and volunteer expertise. They seek to develop structures that can provide sustainability, flexibility, and growth including nodes and network models that allows linkage across varied practice sites. Using technology, the central node can serve a network that can stretch across geographic locations and types of organizations. This new architecture requires support from a variety of sources including law schools and peer support groups all of which enable the sharing of ideas and innovations