Spin Glass Theory and Far Beyond

Abstract

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Neural Activity in Quarks Language: Lattice Field Theory for a Network of Real Neurons

“…For fully connected models, we have and then For models with large connectivity but that are sub-linear in the number of neurons, one can consider with , whereas for finite-dimensional models we have that . From preliminary analysis (we extracted data from Figure 1f of Tkacik et al, 2009 [ 63 ] with G3data and performed a Gaussian fit to find the variances, Figure 4 ), we confirm that the couplings are approximately Gaussian, but the scaling exponent appears to be and not as for the Sherrington–Kirkpatrick model [ 56 , 57 , 58 , 60 , 87 ]. This would be interesting, since the system would admit a thermodynamic limit and still have sufficient connectivity to manage the data with a mean-field theory [ 56 , 57 , 58 , 60 , 87 ].…”

“…From preliminary analysis (we extracted data from Figure 1f of Tkacik et al, 2009 [ 63 ] with G3data and performed a Gaussian fit to find the variances, Figure 4 ), we confirm that the couplings are approximately Gaussian, but the scaling exponent appears to be and not as for the Sherrington–Kirkpatrick model [ 56 , 57 , 58 , 60 , 87 ]. This would be interesting, since the system would admit a thermodynamic limit and still have sufficient connectivity to manage the data with a mean-field theory [ 56 , 57 , 58 , 60 , 87 ]. Also, it would be very interesting to see the full hypermatrix to which the covariance matrix in Figure 1 of Tkacik et al [ 63 ] belongs, and even more interesting would be to fit such a hypermatrix with the field theory presented in this paper.…”

“…The theory in the Lagrangian form allows us to establish a connection with the replica theory [ 60 , 87 ] and since the sum over the kernels is equivalent to a sum over T replicas of the system the replicated system is obtained in the limit (no kinetic term) with simple steps we arrive at the following relations where Z is the partition function associated with the Hamiltonian H and …”

A scientific portrait of Giorgio Parisi: complex systems and much more

“…In 2018, the 40th anniversary of Parisi's first paper on RSB was celebrated in Rome with a conference in which many of the main actors in the use and development of these ideas presented their work. A book with a collection of chapters in which applications of RSB to different fields will soon be published [61]. Though completely useless from a practical point of view the spin-offs of the theoretical work done to describe spin-glasses has been utterly important in very different areas.…”

Multifractality in spin glasses

“…Here, we add a (perhaps) surprising member to the list: the off-equilibrium dynamics of spin-glass systems (17,18). These disordered magnetic alloys have long been regarded as a paradigmatic toy model for the study of glassiness, optimization, biology, financial markets, or social dynamics.…”