Vanishing spin stiffness in the spin-1/2 Heisenberg chain for any nonzero temperature

Whether at the zero spin density m = 0 and finite temperatures T > 0 the spin stiffness of the spin-1/2 XXX chain is finite or vanishes remains an unsolved and controversial issue, as different approaches yield contradictory results. Here we explicitly compute the stiffness at m = 0 and find strong evidence that it vanishes. In particular, we derive an upper bound on the stiffness within a canonical ensemble at any fixed value of spin density m that is proportional to m2L in the thermodynamic limit of chain length L → ∞, for any finite, nonzero temperature, which implies the absence of ballistic transport for T > 0 for m = 0. Although our method relies in part on the thermodynamic Bethe ansatz (TBA), it does not evaluate the stiffness through the second derivative of the TBA energy eigenvalues relative to a uniform vector potential. Moreover, we provide strong evidence that in the thermodynamic limit the upper bounds on the spin current and stiffness used in our derivation remain valid under string deviations. Our results also provide strong evidence that in the thermodynamic limit the TBA method used by X. Zotos [Phys. Rev. Lett. 82, 1764 (1999)] leads to the exact stiffness values at finite temperature T > 0 for models whose stiffness is finite at T = 0, similar to the spin stiffness of the spin-1/2 Heisenberg chain but unlike the charge stiffness of the half-filled 1D Hubbard model.

Cultural circuits of climate change in U.K. broadsheet newspapers, 1985–2003

This article argues for a cultural perspective to be brought to bear on studies of climate change risk perception. Developing the “circuit of culture” model, the article maintains that the producers and consumers of media texts are jointly engaged in dynamic, meaning-making activities that are context-specific and that change over time. A critical discourse analysis of climate change based on a database of newspaper reports from three U.K. broadsheet papers over the period 1985–2003 is presented. This empirical study identifies three distinct circuits of climate change—1985–1990, 1991–1996, 1997–2003—which are characterized by different framings of risks associated with climate change. The article concludes that there is evidence of social learning as actors build on their experiences in relation to climate change science and policy making. Two important factors in shaping the U.K.’s broadsheet newspapers’ discourse on “dangerous” climate change emerge as the agency of top political figures and the dominant ideological standpoints in different newspapers.