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

Orange peel silage in feeding lambs: nutrient intake, performance and economic evaluation

We evaluated the inclusion of orange peel pre-dried silage (SOP) in replacement of corn in lambs’ diet on nutrient consumption, lamb performance and diet effective cost. 20 lambs with an average initial body weight (BW) of 25.37 ± 1,94kg were used, these were confined until they reached 35 kg, their diets presented increasing levels of corn replacement with SOP (0, 33, 66 and 100%). The acid detergent fiber intake was not affected (p> 0.05) by the inclusion of SOP, since the intake of dry matter (DM), organic matter, crude protein, neutral detergent fiber and metabolizable energy (Mcal/kg DM) linearly reduced (p0.05) in function of corn replacement with SOP levels. Still the daily weight gain reduced with the inclusion of SOP, the opposite effect was observed for the days of confinement. The total cost was higher for treatment with 100% of SOP. The net margin of this treatment was the only negative one among the rest. Unlike the treatment with 100% of corn, bran exhibited the highest net margin, followed by a 66% level of substitution. The cost of the workforce accounted for over 60% of the total, reaching 71.16% in the treatment with 100% SOP. The treatment without SOP proved to be the most profitable one from the byproducts substitution levels.Avaliou-se a inclusão da silagem de bagaço de laranja pré-seco (SBL) em substituição ao milho na dieta de cordeiros no consumo de nutriente, desempenho e custo benefício das dietas. Foram utilizados 20 cordeiros com peso corporal (PC) médio inicial de 25,37 ± 1,94kg, estes foram confinados até que atingissem 35 kg, suas dietas possuíram níveis crescentes de SBL em substituição ao milho (0, 33, 66 e 100%). A ingestão de fibra em detergente ácido não foi influenciada (p>0,05) pela inclusão da SBL, já a ingestão de matéria seca (MS), matéria orgânica, proteína bruta, fibra em detergente neutro e energia metabolizável (Mcal/kg MS) reduziram linearmente (p0,05) em função dos níveis de substituição do milho pela SBL. Já o ganho de peso diário reduziu com a inclusão da SBL, efeito contrário foi observado para os dias de confinamento. O custo total foi maior para o tratamento com 100% de SBL. A margem líquida deste foi a única negativa. Contrariamente o tratamento com 100% de farelo de milho exibiu a maior margem líquida, seguido do nível de 66% de substituição. O custo com a mão de obra foi responsável por mais de 60% do custo total, chegando a 71,16% no tratamento com 100% de SBL. O tratamento sem SBL mostrou-se o mais rentável entre os níveis de substituição pelo subproduto