I don't think you can find any refrigeration cycle with no mechanical work input, but absorption refrigeration can be an option with low mechanical work input.

Thermal vapor compression refrigeration cycles work without mechanical compressor, as you know mechanical compressors consume alot of power. However, pumps with relatively less power requirment are used to circulate the refrigerant. Still this kind of cycles have low coefficient of performance, but they have the advantage of using low grade energy sources, such as solar energy or the exhaust of gas turbine.

Do you mean some device like the refrigerators that run on kerosene and have no moving parts, except for two check valves. The kerosene burns and heats up a tube until one valve pops open. Then the tube cools off and the other valve pops open. They don't work nearly as well as an electric refrigerator with a pump, but you don't need electricity to run them. They're also very inefficient, but they are clever.

Thanks all for your contributions,I was considering combining and ejector with an absorption refrigeration using a low grade heat from exhaust of a car,I believe the efficiency will improve a bit.

I think it's a good idea to utilize an ejector in an absorption system. Some points you may need to pay attention: the pressure level in absorption refrigerators is much lower than vapor compression systems in most cases, which may influence the working performance of the ejector. On the other hand,  the first two answers above clearly mentioned the "essential" mechanical work input in absorption systems, yet I think there are possible ways to use heat instead of mechanical work to drive the pump, for example, bubble pump and solar chimney.

As cited in the above answers, absorption and also ejector refrigeration need a few amount of mechanical energy to drive the pump. The problem with these cycles is the overall performance compared to vapor compression refrigeration cycles. It is interesting to combined both cycle, the performance of the combined cycle will be improved ofcourse but it stills lower than classical cycles

Any refrigeration cycle without mechanical work means compressor is eliminated and instead simple vapor absorption cycle (either ammonia refirgeration system or  electrolux refrigeration system or lithium bromide refrigeration system) may be used with low grade of heat energy such as solar power, exhaust from IC engine, energy from waste heet reconvery.

In simple vapor compression cycle, work can be reduced by using pump istead of compressor. However, it gives low  COP   

How about using thermoelectric cooling known as TEC which is the application of the Peltier effect (electric current through dissimilar metals.)  Creates a hot and a cold surface. Works very well and definitely no moving parts or mechanical work. 

You can use Solar Absorption refrigeration system with better refrigerant and absorbant. It doesnt have any moving parts (like pump or compressor etc) . Its an efficient way. And no mechanical work input is required.

Thermoelectric method or vortex tube refrigeration

Absorption refrigeration is an option with "pumping slug".