  We explore a simple lattice field model intended to describe statistical
properties of high frequency financial markets. The model is relevant in the
cross-disciplinary area of econophysics. Its signature feature is the emergence
of a self-organized critical state. This implies scale invariance of the model,
without tuning parameters. Prominent results of our simulation are time series
of gains, prices, volatility, and gains frequency distributions, which all
compare favorably to features of historical market data. Applying a standard
GARCH(1,1) fit to the lattice model gives results that are almost
indistinguishable from historical NASDAQ data.
