The 3-d Random Field Ising Model at zero temperature

We study numerically the zero temperature Random Field Ising Model on cubic lattices of various linear sizes $L$ in three dimensions. For each random field configuration we vary the ferromagnetic coupling strength $J$. We find that in the infinite volume limit the magnetization is discontinuous in $J$. The energy and its first $J$ derivative are continuous. The approch to the thermodynamic limit is slow, behaving like $L^{-p}$ with $p \sim .8$ for the gaussian distribution of the random field. We also study the bimodal distribution $h_{i} = \pm h$, and we find similar results for the magnetization but with a different value of the exponent $p \sim .6$. This raises the question of the validity of universality for the random field problem.Comment: 8 pages, 3 PostScript Figure

Special functions and twisted LL-series

We introduce a generalization of the Anderson-Thakur special function, and we prove a rationality result for several variable twisted $L$-series associated to shtuka functions

Interface mapping in two-dimensional random lattice models

We consider two disordered lattice models on the square lattice: on the medial lattice the random field Ising model at T=0 and on the direct lattice the random bond Potts model in the large-q limit at its transition point. The interface properties of the two models are known to be related by a mapping which is valid in the continuum approximation. Here we consider finite random samples with the same form of disorder for both models and calculate the respective equilibrium states exactly by combinatorial optimization algorithms. We study the evolution of the interfaces with the strength of disorder and analyse and compare the interfaces of the two models in finite lattices.Comment: 7 pages, 6 figure

Excess entropy and central charge of the two-dimensional random-bond Potts model in the large-Q limit

We consider the random-bond Potts model in the large-$Q$ limit and calculate the excess entropy, $S_{\Gamma}$, of a contour, $\Gamma$, which is given by the mean number of Fortuin-Kasteleyn clusters which are crossed by $\Gamma$. In two dimensions $S_{\Gamma}$ is proportional to the length of $\Gamma$, to which - at the critical point - there are universal logarithmic corrections due to corners. These are calculated by applying techniques of conformal field theory and compared with the results of large scale numerical calculations. The central charge of the model is obtained from the corner contributions to the excess entropy and independently from the finite-size correction of the free-energy as: $\lim_{Q \to \infty}c(Q)/\ln Q =0.74(2)$, close to previous estimates calculated at finite values of $Q$.Comment: 6 pages, 7 figure

VIII Jornada sobre la docencia del derecho y las TIC

Els Estudis de dret i ciència política de la Universitat Oberta de Catalunya (UOC) han organitzat la VIII Jornada sobre docència del Dret i les TIC, que es va celebrar el passat 7 de juliol, a la seu de Tibidabo (Barcelona).Les Tecnologies de la Informació i Comunicació (TIC) estan cada vegada més integrades a la docència universitària i cada dia són més els professors que les utilitzen, tant com a eines per comunicar-se i interactuar amb els estudiants com també per gestionar la seva acció docent.The Legal Studies and Political Science department of the Open University of Catalonia (UOC) has organised the 8th Conference on the teaching of Law and ICT, which was held on 2 July at the Tibidabo headquarters (Barcelona).Information and Communication Technology (ICT) is becoming increasingly integrated into university teaching and everyday there are more and more lecturers using it, both as a tool to communicate and interact with the students and also to manage their teaching activity.Los Estudios de Derecho y Ciencia Política de la Universitat Oberta de Catalunya (UOC) han organizado la VIII Jornada sobre docencia del Derecho y TIC, que se celebró el pasado 7 de julio, en la sede de Tibidabo (Barcelona).Las tecnologías de la información y comunicación (TIC) están cada vez más integradas en la docencia universitaria y cada día son más los profesores que las utilizan, tanto como herramientas para comunicarse e interactuar con los estudiantes como también para gestionar su acción docente

Critical and tricritical singularities of the three-dimensional random-bond Potts model for large qq

We study the effect of varying strength, $\delta$, of bond randomness on the phase transition of the three-dimensional Potts model for large $q$. The cooperative behavior of the system is determined by large correlated domains in which the spins points into the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder $\delta>\delta_t$ this percolating cluster coexists with a percolating cluster of non-correlated spins. Such a co-existence is only possible in more than two dimensions. We argue and check numerically that $\delta_t$ is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as $\beta_t/\nu_t=0.10(2)$ and $\nu_t=0.67(4)$. We claim these exponents are $q$ independent, for sufficiently large $q$. In the second-order transition regime the critical exponents $\beta_t/\nu_t=0.60(2)$ and $\nu_t=0.73(1)$ are independent of the strength of disorder.Comment: 12 pages, 11 figure