Finding the Right HeatingAC Thermostat

I have a thermostat in my house that seems to have a very narrow temperature band. This causes it to cycle on and off more frequently that it probably should. I have noticed that when I set the temperature, the digital readout never shows any temperature change which leads me to believe it’s temperature range is < 1 degree. I would like to replace thermostat and need some help deciding which one to buy. Do any of the digital thermostats enable the temperature range to be set? Also, what name is commonly used to describe this parameter.