Optical spin glasses: a new model for glassy systems

1 1 Some topics in spin glass theory 3 1.1 A spin glass introduction: the Ising model . . . . . . . . . . . . . . . 3 1.1.1 Two equivalent Ising models . . . . . . . . . . . . . . . . . . . 6 1.2 Towards spin glasses . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.1 Frustration and complex energy landscape . . . . . . . . . . . 10 1.2.2 Sherrington-Kirkpatrick model . . . . . . . . . . . . . . . . . 12 1.3 Spin glass simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.3.1 Metropolis-Hastings algorithms . . . . . . . . . . . . . . . . . 13 1.3.2 Multi spin flips and cluster algorithms . . . . . . . . . . . . . 16 1.4 The spin autocorrelation function . . . . . . . . . . . . . . . . . . . . 17 1.5 Brief concepts on scaling in spin glass problems . . . . . . . . . . . . 19 2 The theory of the “optical spin glass” 21 2.1 Speckle patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.1.1 Mathematical description of speckle pattern . . . . . . . . . . 25 2.2 The dipole propagator . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.2.1 Multipole expansion in the simple case of one molecule . . . . 31 2.2.2 The dipole approximation . . . . . . . . . . . . . . . . . . . . 33 2.2.3 Explicit expression of the dipole propagator . . . . . . . . . . 36 2.3 The Hamiltonian of the optical spin glass . . . . . . . . . . . . . . . 37 3 Experimental design 42 3.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.1.1 Light source . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 3.1.2 Spatial modulator: the digital micromirror device . . . . . . . 44 3.1.3 Scattering sample . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.1.4 Optical setup and detector . . . . . . . . . . . . . . . . . . . . 46 3.2 Algorithm implementation . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3 Experimental problems and limitations . . . . . . . . . . . . . . . . . 51 3.3.1 Negative defined energy Exposure time feedback . . . . . . . 51 3.3.2 Exposure time feedback . . . . . . . . . . . . . . . . . . . . . 52 i CONTENTS ii 3.3.3 Multi-spin flipping . . . . . . . . . . . . . . . . . . . . . . . . 53 4 Preliminary measurements and checks 54 4.1 Stability analisys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.1.1 Pearson correlation coefficients . . . . . . . . . . . . . . . . . 55 4.2 Measure of couplings . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2.1 Experimental procedure for the measure . . . . . . . . . . . . 60 5 Data analysis 63 5.1 Autocorrelation measure . . . . . . . . . . . . . . . . . . . . . . . . . 63 6 Conclusions and perspectives 70 6.1 Future experimental updates . . . . . . . . . . . . . . . . . . . . . . 71 6.2 Other applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.2.1 p-spin model . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 6.2.2 Hopfield model and neural networks . . . . . . . . . . . . . . 75 Bibliography 80