There are, as mentioned, several brands of these refrigerators available. I installed one from Tundra. Specs on some various models are available here
I put in a TJ22AC, which is 2.2 cubic feet, and was an easy replacement for the size of my cabinet. Note that the current draw shown in the specifications is for running
power consumption. My owners manual stated, and experience confirmed, that the compressor only runs about 20 minutes an hour once it has cooled down. So, you can divide that power consumption essentially by three for "real world" power consumption. You can begin to see how long it can run on a decent battery
Somebody will hopefully correct me if I'm wrong, but if the fridge draws 3.2 amps while running, and runs 1/3 of the time, that would mean it needs about 1.1 amp\hours of battery
power to keep it going. That is about 26.4 amp\hours per 24-hour day. Divide that into about 1/2 of the rated capacity of your deep-cycle battery, and you get approximate days of running on battery. I don't know if that is exactly correct, but my experience says it's not too far off. It also seems that, at this rate of discharge, it would be pretty easy to keep a battery sufficiently charged indefinitely with a solar
I got my fridge from a local boat manufacturer, where a friend works. The link above takes you to one vendor of these units. I know nothing about them, so I can't endorse them, but there is some good information available on their site.
These refrigerators are not particularly cheap (neither are regular RV fridges, as far as that goes), but I would highly recommend them to anyone looking to purchase a fridge for their trailer.