TAM 13 15JuneBologna

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TAM 13-15 June 2007, HPC-EUROPA Bologna Sergio Perez-Gaviro Heisenberg Spin Glass in three dimensions. Isotropy & Anisotropy Weakly Anisotropic Heisenberg Spin Glasses under Magnetic Fields. ( Universidad de Zaragoza & Bifi )

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? It is a collection of spins whose low-temperature state is a frozen disordered state, rather than the kind of periodic or uniform pattern one can find in conventional magnets. TAM 13-15 June 2007, HPC-EUROPA Bologna

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TAM 13-15 June 2007, HPC-EUROPA Bologna

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“Critical Behavior of the three dimensional Ising Spin Gass”, H.G. Ballesteros et el., Phys. Rev. B, 62, 14237 (2000). TAM 13-15 June 2007, HPC-EUROPA Bologna

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I Isotropic Heisenberg spin glass TAM 13-15 June 2007, HPC-EUROPA Bologna

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Introduction the more experimentally interesting case TAM 13-15 June 2007, HPC-EUROPA Bologna

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PBC Bifi cluster (BIFI, Zaragoza) Marenostrum (BSC, Barcelona) Cubic lattice of size L TAM 13-15 June 2007, HPC-EUROPA Bologna

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The Elementary Monte Carlo Step (EMCS) to extrapolate to nearby temperatures we use bias-corrected data reweighting TAM 13-15 June 2007, HPC-EUROPA Bologna

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TAM 13-15 June 2007, HPC-EUROPA Bologna

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Generalizing the standard reweighting method (Alan M. Ferrenberg and Robert H. Swendsen, Phys. Rev. Lett. 61, 2635 (1988)) it is possible to extrapolate measures taken at a temperature T to neighbouring values. where TAM 13-15 June 2007, HPC-EUROPA Bologna

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From the quotients FSS method: TAM 13-15 June 2007, HPC-EUROPA Bologna

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TAM 13-15 June 2007, HPC-EUROPA Bologna

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TAM 13-15 June 2007, HPC-EUROPA Bologna

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Heisenberg spin glass in 3D undergoes a finite temperature transition. A mixture of Heath-Bath and Overrelaxation dynamics allows us to thermalize lattices of size up to L=32. At criticality, spin glass susceptibility scales with the chiral correlation length. Spin-chirality decoupling is ruled out. Logarithmic corrections to scaling are observed. Our results are compatible with a Kosterlitz-Thouless scaling, but they are typical as well of a system with a lower critical dimension barely smaller than three. I. Campos, M. Cotallo-Aban, V. Martin-Mayor, S. Perez-Gaviro, A. Tarancon, “The Spin Glass transition of the three dimensional Heisenberg Spin Glass”, Phy. Rev. Lett. 97, 217204 (2006). TAM 13-15 June 2007, HPC-EUROPA Bologna

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II Anisotropic Heisenberg spin glass TAM 13-15 June 2007, HPC-EUROPA Bologna

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The anisotropic model Decoupling chiral glass and sping glass TAM 13-15 June 2007, HPC-EUROPA Bologna Lomond cluster (EPCC, Edinburgh) Bifi cluster (BIFI, Zaragoza) Marenostrum (BSC, Barcelona)

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The anisotropic model under a magnetic field PBC Cubic lattice of size L TAM 13-15 June 2007, HPC-EUROPA Bologna

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Acknowledgments Adam Carter (Applications Consultant, my contact in EPCC) Davide Marenduzzo (School of Physics, my host in HPC-Programme) Catherine Inglis (HPC-Europa visit co-ordinator, EPCC) Alfonso Tarancón Lafita (thesis director, Universidad de Zargoza) Víctor Martín-Mayor (thesis co-director, Universidad Complutense de Madrid) María Cotallo-Abán (Ph.D. Student, Universidad de Zaragoza) TAM 13-15 June 2007, HPC-EUROPA Bologna

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Bibliography TAM 13-15 June 2007, HPC-EUROPA Bologna

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questions … TAM 13-15 June 2007, HPC-EUROPA Bologna

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TAM 13-15 June 2007, HPC-EUROPA Bologna

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Simulation Model was simulated with a mixture of Heat Bath and Overrelaxation taken from lattice QCD but also effective for frustated spin models • trial element is placed far away from the old value → rather rapid flow through phase space • due to simplicity it is very fast (one HB update is roughly as CPU consuming as 7 overrelaxations) • it may be combined with Parallel Tempering but this is unnecessary at TC • effective for frustated spin models Intuitive arguments in favor of overrelaxation: TAM 13-15 June 2007, HPC-EUROPA Bologna

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Finite Size Scaling (FSS) analysis Advantages of using the quotient method: it is easy to use. arbitary choises on the temperature range are avoided the statistical error estimation is clear it is possible to observe scaling corrections directly by increasing L1 and L2. TAM 13-15 June 2007, HPC-EUROPA Bologna

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TAM 13-15 June 2007, HPC-EUROPA Bologna (S.Miyashita, E.Vincent, Eur. Phys. J, B22, 203 (2001))