Spanning forests and the q-state Potts model in the limit q \to 0

We study the q-state Potts model with nearest-neighbor coupling v=e^{\beta J}-1 in the limit q,v \to 0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating polynomial of spanning forests; physically, it provides information about the Potts-model phase diagram in the neighborhood of (q,v) = (0,0). We have studied this model on the square and triangular lattices, using a transfer-matrix approach at both real and complex values of w. For both lattices, we have computed the symbolic transfer matrices for cylindrical strips of widths 2 \le L \le 10, as well as the limiting curves of partition-function zeros in the complex w-plane. For real w, we find two distinct phases separated by a transition point w=w_0, where w_0 = -1/4 (resp. w_0 = -0.1753 \pm 0.0002) for the square (resp. triangular) lattice. For w > w_0 we find a non-critical disordered phase, while for w < w_0 our results are compatible with a massless Berker-Kadanoff phase with conformal charge c = -2 and leading thermal scaling dimension x_{T,1} = 2 (marginal operator). At w = w_0 we find a "first-order critical point": the first derivative of the free energy is discontinuous at w_0, while the correlation length diverges as w \downarrow w_0 (and is infinite at w = w_0). The critical behavior at w = w_0 seems to be the same for both lattices and it differs from that of the Berker-Kadanoff phase: our results suggest that the conformal charge is c = -1, the leading thermal scaling dimension is x_{T,1} = 0, and the critical exponents are \nu = 1/d = 1/2 and \alpha = 1.Comment: 131 pages (LaTeX2e). Includes tex file, three sty files, and 65 Postscript figures. Also included are Mathematica files forests_sq_2-9P.m and forests_tri_2-9P.m. Final journal versio

Clifford Symington Lord, 1908-1981

Dr. C.S. Lord, formerly Chief Geologist of the Geological Survey of Canada and Chairman of the Board of Governors of The Arctic Institute of North America, died in Ottawa on 4 October 1981. With his passing Canadian earth science lost one of its most able and knowledgeable geologists, especially of the Canadian Shield in the Northwest Territories, as well as one of its most modest and dedicated servants. ... Clifford Lord's broad regional and varied logistical experience, coupled with his demonstrated organizing ability, made him a natural choice in 1954 for Chief Geologist of the Geological Survey - a post he held with distinction for nearly 20 years. This was a period of great expansion and diversification of the Geological Survey program. Although he understood the value of geophysical and geochemical surveys, many of which were begun and carried out during his term as Chief Geologist, he always maintained that geological surveys were the core activity of the Survey and provided the ground truth against which other types of geophysical and geochemical surveys should be judged. While Chief Geologist he introduced a project management system, which though perhaps somewhat cumbersome, was years ahead of its time in the Federal Government. The essence of his system, in a more streamlined form, is used by the Survey today. During most field seasons he visited numerous field parties to learn, first-hand, the geology of various regions of Canada, to become familiar with new techniques, and to observe how the scientists operated in the field. ... Between 1963 and 1971 C.S. Lord carried out many assignments on behalf of the United Nations, Canada's External Aid office and its successor, the Canadian International Development Agency (CIDA). ... As an authority on the geology of the Canadian Shield north of latitude 60° he was elected a Fellow of The Arctic Institute of North America. Furthermore, owing to his Arctic experience, his influential position as Chief Geologist of the Geological Survey, and his administrative talents, he served as a most useful member of the Board of Governors of the Institute, being Chairman in 1960. ... He contributed much to our understanding of the geology of Canada, especially the Precambrian of the Arctic, and provided practical advice for mineral development. Because of his modesty, few except those who followed in his footsteps, appreciated the magnitude and quality of his achievements

A wave of geographical research?

10.1111/j.0129-7619.2005.00218.xSingapore Journal of Tropical Geography262257-26