The instructor pilot was giving dual instruction to a pilot-rated student. He reported that soon after departure, the airplane engine RPM reduced to idle. The pilot verified the throttle was at full power, adequate fuel was in both tanks and subsequently applied carburetor heat, which restored the engine to full power. After 10 seconds the RPM began surging and the pilot then turned the carburetor heat off. He turned the carburetor heat on again and pumped the throttle repeatedly while the power continued to surge until the engine quit and he lost all power. They were unable to restart the engine and landed the airplane in a nearby agricultural field. The airplane came to rest inverted, which resulted in substantial damage to the vertical stabilizer. The engine ran normally on the ground after the airplane was returned to its upright position following the accident. When the temperature and the dewpoint near the time of the accident were plotted on a carburetor icing probability graph, it was revealed that the airplane was likely operating in meteorological conditions conducive to the formation of carburetor icing (for glide power settings). The pilot reported that there were no preaccident mechanical failures or malfunctions with the airplane that would have precluded normal operation.