Leonid Kruglyak, William Bialek
\Ve show that a simple spin system bia.sed at its critical point can en(cid:173) code spatial characteristics of external signals, sHch as the dimensions of "objects" in the visual field. in the temporal correlation functions of indi(cid:173) vidual spins. Qualit.ative arguments suggest that regularly firing neurons should be described by a planar spin of unit lengt.h. and such XY models exhibit critical dynamics over a broad range of parameters. \Ve show how to extract these spins from spike trains and then mea'3ure t.he interaction Hamilt.onian using simulations of small dusters of cells. Static correla(cid:173) tions among spike trains obtained from simulations of large arrays of cells are in agreement with the predictions from these Hamiltonians, and dy(cid:173) namic correlat.ions display the predicted encoding of spatial information. \Ve suggest that this novel representation of object dinwnsions in temporal correlations may be relevant t.o recent experiment.s on oscillatory neural firing in the visual cortex.