Strong-Disorder Paramagnetic-Ferromagnetic Fixed Point in the Square-Lattice ±J Ising Model

Toldin, Francesco Parisen; Pelissetto, Andrea; Vicari, Ettore

doi:10.1007/s10955-009-9705-5

Cited by 39 publications

(63 citation statements)

References 62 publications

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“…Nevertheless, for sufficiently strong disorder the model undergoes a continuous phase transition between a paramagnetic and a glassy phase, with a multicritical point separating the paramagnetic, ferromagnetic, and glassy phases [59], Another example is provided by the 2D ± J Ising model. Here, weak disorder is marginally irrelevant, so that for weak disorder the critical behavior is controlled by the "pure" 2D Ising fixed point [61], Nevertheless, the model exhibits also a strong-disorder fixed point [62,63] and a multicritical point, which in the phase diagram separates the transition line in the Ising UC and the one in the strong-disorder UC [63,64],…”

Section: Introductionmentioning

confidence: 99%

Critical Casimir force in the presence of random local adsorption preference

Toldin

2015

Phys. Rev. E

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We study the critical Casimir force for a film geometry in the Ising universality class. We employ a homogeneous adsorption preference on one of the confining surfaces, while the opposing surface exhibits quenched random disorder, leading to a random local adsorption preference. Disorder is characterized by a parameter p, which measures, on average, the portion of the surface that prefers one component, so that p=0,1 correspond to homogeneous adsorption preference. By means of Monte Carlo simulations of an improved Hamiltonian and finite-size scaling analysis, we determine the critical Casimir force. We show that by tuning the disorder parameter p, the system exhibits a crossover between an attractive and a repulsive force. At p=1/2, disorder allows to effectively realize Dirichlet boundary conditions, which are generically not accessible in classical fluids. Our results are relevant for the experimental realizations of the critical Casimir force in binary liquid mixtures.

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Section: Introductionmentioning

confidence: 99%

Critical Casimir force in the presence of random local adsorption preference

Toldin

2015

Phys. Rev. E

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“…We also test the fit by using different data groups, for example L 32 and L 64. All test [27,28] 0.85 Duality analysis [32] 0.889 972 Duality analysis [33] 0.890 813 pTRG 0.890 830(22) Monte Carlo [29] 0.890 81(7) Monte Carlo [43] 0.890 83 (3) are consistent with each other, except the data of L = 8, which has strong finite size effect so that we discard it in all fits. The susceptibilities χ are checked by using different differential steps δh ranging from 10 −6 to 10 −3 .…”

Section: Numerical Resultsmentioning

confidence: 78%

Topologically invariant tensor renormalization group method for the Edwards-Anderson spin glasses model

2014

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Tensor renormalization group (TRG) method is a real space renormalization group approach. It has been successfully applied to both classical and quantum systems. In this paper, we study a disordered and frustrated system, the two-dimensional Edwards-Anderson model, by a new topological invariant TRG scheme. We propose an approach to calculate the local magnetizations and nearest pair correlations simultaneously. The Nishimori multicritical point predicted by the topological invariant TRG agrees well with the recent Monte Carlo results. The TRG schemes outperform the mean-field methods on the calculation of the partition function. We notice that it might obtain a negative partition function at sufficiently low temperatures. However, the negative contribution can be neglected if the system is large enough. This topological invariant TRG can also be used to study three-dimensional spin glass systems.

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“…The so-called strongdisorder fixed point [16] is missing and the crossing is not associated with flows towards the FM and strong-disorder fixed points.…”

Section: Four-square-cell Cluster (Sq 4 )mentioning

confidence: 98%

“…The projection matrix defined above does not preserve the three-state permutation symmetry on the Potts axis (16), as an exact RG would do. The distance of the fixed point P * from the Potts axis can then be used as an indicator of the error made with the cluster approximation used to build the block RG transformation.…”

Section: A Ordered 2d Beg Modelmentioning

confidence: 98%

“…5. The block RG transformation is performed by summing in the partition sum over all possible configurations of the spins of the cells s i=1,..., 16 for fixed block-spins, The 16 spins of the SQ 4 cluster, together with the intercell interactions from periodic boundary conditions, form a 4 × 4 array of 4-spin cells. The block RG transformation generates, besides nearest-neighbor interactions, also next-nearestneighbor interactions and "plaquette" interactions.…”

Section: Four-square-cell Cluster (Sq 4 )mentioning

confidence: 99%

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Small-cluster renormalization group in Ising and Blume-Emery-Griffiths models with ferromagnetic, antiferromagnetic, and quenched disordered magnetic interactions

2014

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The Ising and Blume-Emery-Griffiths (BEG) models' critical behavior is analyzed in two dimensions and three dimensions by means of a renormalization group scheme on small clusters made of a few lattice cells. Different kinds of cells are proposed for both ordered and disordered model cases. In particular, cells preserving a possible antiferromagnetic ordering under renormalization allow for the determination of the Néel critical point and its scaling indices. These also provide more reliable estimates of the Curie fixed point than those obtained using cells preserving only the ferromagnetic ordering. In all studied dimensions, the present procedure does not yield a strong-disorder critical point corresponding to the transition to the spin-glass phase. This limitation is thoroughly analyzed and motivated.

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Strong-Disorder Paramagnetic-Ferromagnetic Fixed Point in the Square-Lattice ±J Ising Model

Cited by 39 publications

References 62 publications

Critical Casimir force in the presence of random local adsorption preference

Critical Casimir force in the presence of random local adsorption preference

Topologically invariant tensor renormalization group method for the Edwards-Anderson spin glasses model

Small-cluster renormalization group in Ising and Blume-Emery-Griffiths models with ferromagnetic, antiferromagnetic, and quenched disordered magnetic interactions

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