The Master, Paul Thomas Anderson, 144 mins (15)

Anderson's latest film is a puzzling, slippery, and brilliantly acted portrait of post-war American damage and disintegration

Joaquin Phoenix plays a brittle anti-hero who falls in with a cult (Chuck Zlotnick)

There's little genuine mystery in American cinema today; and what there is has pretty much been cornered by writer-director Paul Thomas Anderson. His hugely ambitious youthful features Boogie Nights and Magnolia marked him out as an inheritor of Robert Altman, with splashes of Tarantino's pop-culture exuberance. But then 2007's There Will Be Blood proved a statement of such command – and such seriousness about US history – that it instantly changed everyone's picture of Anderson as just a callow prodigy. Now The Master maintains the enigmatic tone of Blood, and pushes it into elliptical new territory. It's an elusive film, sketchy in places to the point of seeming unfinished, but overall as bewitching a hallucination as Anderson has ever conjured.

Not that The Master is really so mysterious, not on the surface. To all intents and purposes, it's clear what this drama is about. It's the story of a spiritually lost man falling under the spell of a charismatic guru, the leader of a burgeoning cult-like organisation – a figure who looks for all the world like L Ron Hubbard, the founder of Scientology. The lost soul is Freddie Quell (Joaquin Phoenix), who leaves the US Navy at the end of the Second World War in a state of battle-scarred shock, his only reliable talents being his readiness to throw a punch and his skill at improvising high-risk cocktails using materials such as paint thickener and missile fuel.

Running from the law, Freddie one day finds himself, as if by magic, aboard a pleasure boat lorded over by the affable Lancaster Dodd (Philip Seymour Hoffman). Dodd describes himself as "a hopelessly inquisitive man ... a scientist and a connoisseur". Freddie becomes a loyal acolyte of Dodd's new spiritual path, the Cause, ever ready to rough up those who dare question the master. We can see what's in it for Freddie: a home, money, approval. But why does Dodd want him around? None of the film's possible answers quite explains it, and that's what makes this perverse father-son, tyrant-subject, master-servant relationship so troubling.

The Master is certainly no standard Hollywood roman à clef about Scientology. It's more about Freddie the follower than about Dodd the leader, and is strangely slippery. Its shape, coherent though it is, seems to dissolve as you watch: it's a Great American Novel with chapters torn out and odd pages out of order. There's nothing about Dodd's past. (Where did he come from? How did he devise his cockamamie gospel? How did he talk all these deluded toffs into bankrolling him?) But there's much about Quell's history: his war in the South Pacific (presented like a homoerotic remake of Terrence Malick's The Thin Red Line), his collapse, the apparent "Rosebud"-like core of meaning in his life – namely, the girl who got away. While the overbearing Dodd seems a man of absolute presence and coherence (his selling point as a prophet), Freddie is all fragmentation, all history – and perhaps no real present or future.

The film offers a compelling depiction of post-war American disorder: of a damaged generation of men trying to reintegrate themselves into the world. It's also very much about post-war technologies of measuring the soul: from the Rorschach tests that Freddie is given by an armed forces shrink to the various bogus "applications" that Dodd puts him through.

And it's a film about acting. One of the trials that Freddie faces is oddly like a drama school exercise and involves him pacing repeatedly up and down a room. Anderson audaciously foregrounds the act of performance at high intensity, and at sometimes confrontational length.

If There Will Be Blood allowed Daniel Day-Lewis to stride brazenly about the screen like a manic titan, The Master is much more a duet, or a duel. Hoffman is magnificent – knowingly magnificent, which is the point – as a man ruthlessly exploiting his charisma. Whatever Ron Hubbard may have been like in person, it is perhaps no accident that Dodd most recalls Orson Welles – the raconteur, the manipulator, the terroriser of crowds.

As for Phoenix, it's hard to shake off memories of the recent faux-documentary I'm Still Here, in which the actor apparently staged a mental breakdown as performance art. In The Master, Phoenix seems to have internalised his real or feigned collapse, and has created American cinema's most damaged anti-hero since Travis Bickle. Damage is writ in Freddie's face and body, in his grimaces of furious reticence, and in that strange hunched hands-on-hips posture, as if the psychic agony began right at the base of his spine.

Is Anderson's latest the masterpiece it seems at first look? I don't know: I'd like a second viewing, ideally projected in 70mm, the way that the director of photography, Mihai Malaimare Jnr, shot it. The Master is certainly a tantalising creation, full of strange elements that refuse to fit a realistic context. I'm thinking of Freddie appearing to slip in and out of time frames; of the visual non-sequiturs such as the sedate party that seems to become a nude orgy in the making; and of the way that Amy Adams, as Dodd's wife, suddenly reveals a terrible, steely power beneath her coy exterior. No less slippery is Jonny Greenwood's score, his most accomplished yet, which veers between pulsating jazz bass, glimmering Debussy pastiche and blocks of traumatised strings. Whatever else it may be, The Master is one of those rare films that tells us to go away and think, and dream … then, when you're ready, come back and start again.

French cinema's It girl Léa Seydoux and young prodigy Kacey Mottet Klein star in Sister, a drama about a boy struggling for survival at a Swiss ski resort. Elena is a cool, restrained exercise in Russian noir from director Andrey Zvyagintsev (of The Return fame).