Finite-size investigation of scaling corrections in the square-lattice three-state Potts antiferromagnet square-lattice three-state Potts antiferromagnet

We investigate the finite-temperature corrections to scaling in the three-state square-lattice Potts antiferromagnet, close to the critical point at T=0. Numerical diagonalization of the transfer matrix on semi-infinite strips of width $L$ sites, $4 \leq L \leq 14$, yields finite-size estimates of the corresponding scaled gaps, which are extrapolated to $L\to\infty$. Owing to the characteristics of the quantities under study, we argue that the natural variable to consider is $x \equiv L e^{-2\beta}For the extrapolated scaled gaps we show that square-root corrections, in the variable$x$, are present, and provide estimates for the numerical values of the amplitudes of the first-- and second--order correction terms, for both the first and second scaled gaps. We also calculate the third scaled gap of the transfer matrix spectrum at T=0, and find an extrapolated value of the decay-of-correlations exponent,$\eta_3=2.00(1)$. This is at odds with earlier predictions, to the effect that the third relevant operator in the problem would give$\eta_{{\bf P}_{\rm stagg}}=3$, corresponding to the staggered polarization.Comment: RevTex4, 5 pages, 2 .eps figures include

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

Going off-road: The Stellenbosch Winelands as a mountain biking destination

Research on mountain biking in human geography and the social sciences, particularly in Africa and South Africa, is underexplored. In 2015, the Western Cape government earmarked cycling as an important driver of economic growth, yet it remains unclear what aspects of the area contribute towards this notion. This study seeks to investigate the product offering and growth of mountain biking in Stellenbosch, South Africa, in order to provide a platform for and more research into the tourist offering for this lifestyle sport. The research is set out to provide a brief overview of the historical development of mountain bikes and the sport of mountain biking on an international scale, then narrows it down to the Western Cape of South Africa, and finally examines the town of Stellenbosch as a case study. The case study is presented using an analysis of the existing strengths, weaknesses, opportunities and threats of the area as a mountain biking destination. The findings presented originate from a snowballing process of personal in-depth interviews with 15 stakeholders and participants in the Stellenbosch mountain biking community, including professional and amateur cyclists, professionals in the bicycle industry and other people connected to mountain biking through employment or recreational pursuits. Findings include major opportunities for economic growth through tourism, as well as in social upliftment and personal wellbeing for participants across all demographics. Challenges faced include destruction and damage of trails due to fire as well as escalating and aggravated incidences of crimes against mountain bikers. In conclusion, suggestions for further research are proffered.Keywords: Lifestyle sports, mountain biking, South Africa, Stellenbosch, touris

Analgesia e ação antiinflamatória da Arnica montana 12CH comparativamente ao cetoprofeno em cães Analgesic and anti-inflammatory effects of Arnica montana 12CH in comparison with ketoprofen in dogs

Objetivou-se avaliar os efeitos analgésico e antiinflamatório da Arnica montana 12CH comparativamente ao cetoprofeno em cadelas submetidas à ovariossalpingohisterectomia (OSH). Foram avaliadas 16 cadelas, distribuídas aleatoriamente em dois grupos de oito animais cada, tratados por via oral com 1mg kg-1 de cetoprofeno (TC) e com cinco glóbulos de Arnica montana 12CH (TA). Decorridos 60 minutos, os animais foram tranquilizados com acepromazina (0,05mg kg-1, IV), seguindo-se indução e manutenção anestésica com propofol (5mg kg-1, IV) e isofluorano, respectivamente. Foram mensurados: frequência cardíaca, frequência respiratória, pressão arterial sistólica, concentração final expirada de dióxido de carbono, concentração final expirada de isofluorano, variáveis hemogasométricas, concentração sérica de cortisol, grau de analgesia e de inflamação. Em casos de analgesia insuficiente, foi realizada suplementação com morfina (0,5mg kg-1, IM). A estatística foi realizada com ANOVA e teste de Tukey (P<0,05). Estabilidade cardiorrespiratória foi observada em ambos os tratamentos durante a OSH. Não houve diferença entre os tratamentos em relação ao grau de analgesia e de inflamação. Analgesia de resgate foi necessária em dois animais de cada grupo. Conclui-se que a Arnica montana 12 CH confere efeitos analgésico e antiinflamatório semelhantes aos do cetoprofeno, sendo uma opção segura e efetiva para cadelas submetidas à OSH.<br>This study aimed to evaluate the analgesic and anti-inflammatory effects of Arnica montana 12CH comparatively to ketoprofen in dogs undergoing ovariohysterectomy. Sixteen female dogs were randomly distributed in two groups of eight animals and received 1mg kg-1 of ketoprofen (TC) and 5 globules of Arnica montana 12CH (TA) by oral route. After 60 minutes, the dogs were sedated with acepromazine (0.05mg kg-1, IV), followed by anesthetic induction with propofol (5mg kg-1 IV) and maintained with isoflurane. Heart rate, respiratory rate, systolic blood pressure, arterial blood gases, serum cortisol concentration and degree of analgesia and inflammation were measured. Additional morphine (0.5mg kg-1IM) was given when the analgesia was insufficient. Statistical analyses were performed by ANOVA and Tukey tests (P<0.05). Cardiopulmonary stability was observed in both treatments during the surgery. The degree of analgesia and inflammation did not differ between groups. Rescue analgesia was administered to two dogs from each group. It was concluded that Arnica montana 12CH provides similar analgesic and anti-inflammatory effects when compared with ketoprofen, suggesting that this treatment is a safe and effective option to dogs undergoing ovariohysterectomy