Recent Advances on Low-temperature Spin Glasses and Combinatorial Problems

Stefan Boettcher, Physics, Emory University

Some recent developments regarding the low-temperature regime of spin glasses will be reviewed. Mean-field theory has been successfully extended to long-range systems of finite connectivity, with significant impact especially on combinatorial decision problems. Evidence on finite-dimensional systems seems to suggest significant discrepancies with mean-field predictions. Some high-precision numerical results are reported that may help to sharpen existing models.