As discussed before, for the smaller value of L we have pronounced finite-size effects. In the clean case, a reweighting technique is combined with a careful extrapolation of the data to infinite time to determine with high accuracy the critical behavior in the three-dimensional directed percolation universality class. 5). 'Percolation and Cluster Size', by J.W. We This is satisfied by the Metropolis algorithm [20], c(s;i)=min{1,exp(−βΔH)}, for instance [18]. Niemeijer and J.M.J. . Martin. The diffusion-maps method is a kind of manifold learning algorithm, which tries to find a lower-dimensional representation of data. T. Jorg, H. G. Katzgraber and F. Krzakala, Phys. Rev. Square Lattice with Extra-Vertex Boundary Conditions, A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas, View 7 excerpts, cites methods and background, View 3 excerpts, cites methods and background, By clicking accept or continuing to use the site, you agree to the terms outlined in our. B, N. Crokidakis and F. D. Nobre, Phys. “I think it’s really important to discuss the vision and the surprises”, Segev comments, “[we want] to be able to use this method to identify phase transitions in quantum many-body systems – where the theory is incomputable, and it is virtually impossible to make real predictions for the experiments.”. The avalanche size distributions of spreading events exhibit robust power-law tails. Standard deviation σQ of the average coordination number [Q]µ of blocks of size L b for a random Voronoi lattice and a square lattice with 50% bond dilution (100 lattices with 5000 2 sites each). Following the success of the Ising model to capture the essential physics of complex systems, several lattice models have been proposed [8]. Phase transitions in lattice systems with random local properties @inproceedings{Kasteleyn1969PhaseTI, title={Phase transitions in lattice systems with random local properties}, author={P. W. Kasteleyn and C. M. Fortuin}, year={1969} } irrelevant and the rare-region classification which predicts unconventional Lett. We have analyzed the following values of the parameters: σ=0.0,0.1,0.2,0.3,0.4 and 0.5, all of them in the range 0.0<726f56ff07c0c07fb824c94e1aaad8ac>]
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Please enter the e-mail address you used to register to reset your password, Thank you for registering with Physics World 8 we show the magnetization per spin versus the temperature (left side) and the best collapse of the curves (right side), based on the standard FSS forms. Thus, extensions of this work concerning on MC simulations of the RFISG in the presence of random fields generated according to the double-gaussian distribution, for the equilibrium (quenched and annealed variables) and nonequilibrium cases, would be of great interest to elucidate the existence of the AT line in equilibrium systems with short-range interactions and to obtain more results for nonequilibrium spin glasses. That study showed a rich behavior of the system, with continuous and first-order phase transitions as well as a change in the concavity of the Almeida-Thouless (AT) line [30], which was experimentally verified in the diluted antiferromagnets FexZn1−xF2 [31]. 5 we show the results of magnetization versus the temperature for L=32,64,128,256 and 512. When any amount, including infinitesimal, frustration is introduced, the chaotic rescaling of local interactions occurs in the spin-glass phase. We will show that this rapid fluctuation of the random variables hi during the time evolution of the system lead to a first-order transition between the ordered and the disordered phases for high values of the random-field intensity ho, in opposition of the continuous transition that was found for small ho. B. Haris and M. Schwartz, Phys. 0000008476 00000 n
We consider both continuum and discrete random geometries that are commonly studied in classical percolation theory. The calculated runaway exponent yR of the renormalization-group flows decreases with increasing frustration to yR=0 when the spin-glass phase disappears. The exponent β, which characterizes the behavior of the magnetization near the critical point Tc, was calculated to give us the best collapse of the magnetization curves. The clean (without disorder) model exhibits three phases: inactive (absorbing), active symmetric, and active asymmetric, where the latter exhibits distinct sublattice densities. wandering exponent of $\omega=1/4$. 'Conformational Phase Transitions in a Macromolecule: Exactly Solvable Models', by F.W. [1], Volumes 1-6 were edited by Cyril Domb and Melville S. Green, and after Green's death, volumes 7-20 were edited by Domb and Joel Lebowitz.[1][2]. In statistical mechanics, however, only its dual, the Delaunay triangulation, has been considered in the investigation of critical phenomena. To summarize the results discussed along this paper, we show in Fig. Carlos, J.F. Although the RFIM defined in terms of a single gaussian probability distribution is physically acceptable, it usually leads only to continuous phase transitions, either within mean-field [21, 22, 23], or standard short-range-interaction approaches [24, 25]. The stability of clean critical points is Specialists in statistical physics and other related fields will greatly benefit from this publication. (2) with c(s;x) describing a competing process [18]. 4 we show the magnetization per spin as a function of the temperature for L=128, σ=0.2 and some typical values of ho. 2]. such model, quantum three-color Ashkin-Teller model and show that the quantum 0000008222 00000 n
'Asymptotic Analysis of Power-Series Expansions', by A.J. Lett. In Fig. These findings resolve the apparent contradiction between the Rev. The system therefore undergoes a phase transition in which \(M\) changes discontinuously as it crosses over the coexistence curve at \(H=0\).
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