Is consciousness a physical phenomenon? If it's not physical, then what is it? Is it an algorithm? Well, for one, there is no precedent. Nothing else in the material world is purely an algorithm...except maybe a computer running an algorithm...
I don't see the distinction you're making. I think I want to say "ok, so nothing is purely an algorithm". A computer relies on the rest of the universe just like your brain and I guess it's therefore a "physical phenomenon"?
In order to draw a distinction, perhaps one could say that a "pure algorithm" is something that can run on "many" substrates, so the difference between a "pure algorithm" and a "physical phenomenon" is about the variance in the substrates maybe? But everything is physical. Statements about abstractions are statements about patterns of physical things.
Interestingly enough, this may not be entirely true. There are some fundamental relationships between computation, information, and entropy, that, in the limit of computational and representational perfection, probably would require exactly the amount of input energy as the ice-cube itself would to melt.
Now, you might argue that this is a pedantic attack on your argument. It's not though. The real point is that the laws of physics often seem to have grander symmetries and transformation laws than observable at first glance, and the universe has very clever ways of enforcing these symmetries in what appear to be very different contexts, but are indicative of less intuitive symmetry laws.